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Hana sold 4/7 of her stamp collection for $28. How much would she have earned from selling the entire collection?

##Solution## Hana sold 4/7 of her collection for $28, so 1/7 of her collection represents: 28/4 = $<<28/4=7>>7. And as a result, the entire collection represents: 7 * 7 = $<<7*7=49>>49. #### 49

Mr. Finnegan has 3 tanks with a capacity of 7000 gallons, 5000 gallons, and 3000 gallons, respectively. If he fills the first tank up to 3/4 full, the second tank with water up to 4/5 of its capacity, and the third tank up to half of its capacity, how many gallons in total are in the tanks?

##Solution## The capacity of the first tank is 7000 gallons, and if it is filled up to 3/4 full, it carries 3/4*7000 = 5250 gallons. When the second tank is filled up to 4/5 of its capacity, it carries 4/5*5000 = <<4/5*5000=4000>>4000 gallons. The total amount of water in the first two tanks is 5250+4000 = <<5250+4000=9250>>9250 gallons. If Mr. Finnegan fills the third tank with water up to half its capacity, the tank fills up with 1/2*3000 = <<1500=1500>>1500 gallons. In total, the three tanks have 9350+1500 = <<9350+1500=10850>>10850 gallons of water. #### 10850

In ancient China, soldiers positioned in beacon towers along the Great Wall would send smoke signals to warn of impending attacks. Since the towers were located at 5 kilometer intervals, they could send a signal the length of the Great Wall. If the Great wall was 7300 kilometers long, and every tower had two soldiers, what was the combined number of soldiers in beacon towers on the Great Wall?

##Solution## If there were beacon towers every 5 kilometers along the 7300 kilometer length of the Great Wall, then there were 7300/5=<<7300/5=1460>>1460 beacon towers. If every tower had two soldiers, then there were a total of 1460*2=<<1460*2=2920>>2920 soldiers in beacon towers along the Great Wall. #### 2920

James trains for the Olympics. He trains twice a day for 4 hours each time for all but 2 days per week. How many hours does he train a year?

##Solution## He trains 4*2=<<4*2=8>>8 hours per day He trains 7-2=<<7-2=5>>5 days So he trains 8*5=<<8*5=40>>40 hour per week That means he trains 40*52=$<<40*52=2080>>2080 #### 2080

Tom charges a fee of $100 a day to search for an item for the first 5 days and then $60 per day for every day after that. How much did it cost for him to look for an item for 10 days?

##Solution## The first 5 days cost 5*100=$<<5*100=500>>500 He gets 10-5=<<10-5=5>>5 days on discount He paid 5*60=$<<5*60=300>>300 at the discounted rate So in total he pays 500+300=$<<500+300=800>>800 #### 800

Agatha has $60 to spend on a new bike. She spends $15 on the frame, and $25 on the front wheel. What does she have left, in dollars, to spend on a seat and handlebar tape?

##Solution## Agatha spends 15+25=<<15+25=40>>40 dollars. Agatha has 60-40=<<60-40=20>>20 dollars left. #### 20

In today's field day challenge, the 4th graders were competing against the 5th graders. Each grade had 2 different classes. The first 4th grade class had 12 girls and 13 boys. The second 4th grade class had 15 girls and 11 boys. The first 5th grade class had 9 girls and 13 boys while the second 5th grade class had 10 girls and 11 boys. In total, how many more boys were competing than girls?

##Solution## When you add up all the girls from all 4 classes, you had 12+15+9+10= <<12+15+9+10=46>>46 girls When you add up all the boys from all 4 classes, you had 13+11+13+11 = <<13+11+13+11=48>>48 boys There are 48 boys and 36 girls so 48-46 = 2 more boys #### 2

The school store had a sale on pencils. Ten students bought pencils. The first two students bought 2 pencils each. The next six students bought three pencils each and the last two students only bought one pencil each. How many pencils were sold?

##Solution## The first students bought 2*2=<<2*2=4>>4 pencils The next 6 students bought 6*3=<<6*3=18>>18 pencils The last two students bought 1+1=<<1+1=2>>2 pencils In total the store sold 4+18+2=<<4+18+2=24>>24 pencils #### 24

A storm dropped 5 inches of rain in the first thirty minutes. In the next 30 minutes, the hurricane dropped half that amount of rain. It then dropped 1/2 inch of rain for the next hour. What was the average rainfall total for the duration of the storm?

##Solution## The storm dropped 5 inches then half that amount so 5/2 = <<5/2=2.5>>2.5 inches The next hour the storm dropped 1/2 inch of rain for 1 hour so 1*.5 = <<1*.5=.5>>.5 inches All total the storm dropped 5 inches + 2.5 inches + .5 inch for = <<5+2.5+.5=8>>8 inches It rained for 2 hours total so 8/2 = <<8/2=4>>4 inches of rain per hour #### 4

Bill is hoarding toilet paper in fear of another pandemic. Bill goes to the bathroom three times a day and uses 5 squares of toilet paper each time. If Bill has 1000 rolls of toilet paper and each roll has 300 squares of toilet paper, how many days will his toilet paper supply last?

##Solution## First find the total number of squares Bill's hoard has: 1000 rolls * 300 squares/roll = <<1000*300=300000>>300000 squares Then find the number of squares Bill uses each day: 5 squares/time * 3 times/day = <<5*3=15>>15 squares/day Now divide the total number of squares by the number of squares Bill uses each day to find how many days his hoard will last: 300000 squares / 15 squares/day = <<300000/15=20000>>20000 days #### 20000

Boris has 24 books and he donates a fourth of his books to the library. Cameron has 30 books and he donates a third of his books to the library. After donating their books, how many books in total do Boris and Cameron have together?

##Solution## Boris donates 24 / 4 = <<24/4=6>>6 books Then Boris has a total of 24 - 6 = <<24-6=18>>18 books Cameron donates 30 / 3 = <<30/3=10>>10 books Then Cameron has a total of 30 - 10 = <<30-10=20>>20 books Altogether, Boris and Cameron have 18 + 20 = <<18+20=38>>38 books #### 38

Kevin has a tree growing in his garden that is currently 180 inches tall. That is 50% taller than it was when he planted it there. How tall was the tree, in feet, then?

##Solution## Since it is 50% taller, then 180 inches is 100% + 50% = 150% of its height then. So each 1% is equal to 180/150 = <<180/150=1.2>>1.2 inches. So, its height then was 1.2 x 100% = 120 inches. Since 1 foot is equal to 12 inches, then 120 inches is equal to 120/12 = <<120/12=10>>10 feet. #### 10

Marcus had 18 pebbles. He skipped half of them across the lake, but Freddy gave him another 30 pebbles. How many pebbles does Marcus have now?

##Solution## Marcus had 18/2 = <<18/2=9>>9 pebbles left. After Freddy gave him more, he has 9 + 30 = <<9+30=39>>39 pebbles. #### 39

Company A and Company B merge. Company A receives 60% of the combined profits under the new merger, and company B receives 40% of the profits. If company B gets a total of $60000 in profit, how much does company A get?

##Solution## Let the total profit of both companies be denoted by x. Therefore, 40% * x = 0.4 * x = $60000 So x = $60000 / 0.4 = $150000. If Company B gets 60 % of the profits, it gets 60% of $150000, which is 0.6 * $150000 = $<<0.6*150000=90000>>90000. #### 90000

Musa is the class teacher of a class of 45 students. He wants to split them into three groups by age. If a third of the class is under 11 years, and two-fifths are above 11 but under 13, how many students will be in the third group (13 years and above)?

##Solution## The first group is a third of the class which is (1/3)*45 = <<1/3*45=15>>15 students There are 15 students in the first group, so there are 45-15 = <<45-15=30>>30 students The second group is two-fifths of the class which is (2/5)*45 = <<2/5*45=18>>18 students There are 18 in the second group so there are 30-18 = <<30-18=12>>12 students left in the third group #### 12

It took Dad 5 more than twice as long to vacuum upstairs then to vacuum downstairs. He vacuumed for a total of 38 minutes. How many minutes did he vacuum upstairs?

##Solution## Let D = time in minutes to vacuum downstairs Upstairs = 2D + 5 minutes 3D + 5 = 38 3D = 33 D = <<11=11>>11 minutes Upstairs = (2 * 11) + 5 = <<(2*11)+5=27>>27 minutes Dad took 27 minutes to vacuum upstairs. #### 27

Ryan wants to take 5 peanut butter sandwiches to the beach. If each sandwich consists of 3 slices of bread how many slices does Ryan need to make 5 sandwiches?

##Solution## To make 1 sandwich, you need 3 slices so Ryan needs 1*3= <<1*3=3>>3 slices to make one sandwich. Since it takes 3 slices to make a sandwich, and Ryan wants 5 sandwiches to take to the beach he needs 3*5= <<3*5=15>>15 slices. #### 15

Max fills up water balloons for 30 minutes at a rate of 2 water balloons every minute. Max’s friend Zach fills up water balloons for 40 minutes at a rate of 3 water balloons every minute. In the process, 10 of the water balloons pop on the ground. How many filled water balloons do Max and Zach have in total?

##Solution## Max fills 30 * 2 = <<30*2=60>>60 water balloons Zach fills 40 * 3 = <<40*3=120>>120 water balloons Max and Zach have a total of 60 + 120 - 10 = <<60+120-10=170>>170 water balloons #### 170

Josh found out that 7 bottle caps weigh exactly one ounce. Josh's entire bottle cap collection weighs 18 pounds exactly. How many bottle caps does Josh have in his collection?

##Solution## Josh's collections weights 18 * 16 = <<18*16=288>>288 ounces. Josh's collection contains 288 * 7 = <<288*7=2016>>2016 caps #### 2016

Tapanga and Corey have 66 candies together. However, Tapanga has 8 more candies than Corey. How many candies does Corey have?

##Solution## Let x = the total number of candies Corey has. x + 8 = the total number of candies Tapanga has. The equation for the total number of candies is x + (x + 8) = 66 Combining like terms, we get 2x + 8 = 66 Subtracting 8 from both sides, we get 2x = 58 Dividing both sides by 2, we get x = <<29=29>>29, so Corey has 29 candies. #### 29

Nikola is saving up for a bag of ant food before he can start his ant farm. He wants 400 ants in his farm. Each ant needs 2 ounces of food. Every ounce of ant food costs $.1. Nikola is saving up by raking leaves. He charges $5 to start a job and then he charges by the leaf. Each leaf he rakes costs 1 penny. He finally saved up enough money after he raked 6,000 leaves. How many jobs did he complete?

##Solution## The ants will need 800 ounces of food because 400 x 2 = <<400*2=800>>800 The ant food will cost $80 because 800 x .1 = <<800*.1=80>>80 He has earned $60 from the leaves he has raked because 6000 leaves * $0.01/leaf = $<<6000*0.01=60>>60 He earned $20 from all his jobs because 80 - 60 = <<80-60=20>>20 He completed 4 jobs because 20 / 5 = <<20/5=4>>4 #### 4

А Senior Center is hosting a bingo night. $2,400 in prize money will be given away. The first winner of the night will receive a third of the money. The next ten winners will each receive a 10th of the remaining amount. How many dollars will each of the next ten winners receive?

##Solution## The first winner will receive 2400 / 3 = $<<2400/3=800>>800. There will be 2400 - 800 = $<<2400-800=1600>>1600 left. The other winners will receive 1600 / 10 = $<<1600/10=160>>160 each. #### 160

Mark is filling a punch bowl that can hold 16 gallons of punch. He fills it part way, then his cousin comes along and drinks half the punch in the bowl. Mark starts to refill the bowl and adds 4 more gallons, but then his friend Sally comes in and drinks 2 more gallons of punch. After that, Mark has to add 12 gallons of punch to completely fill the bowl. How much punch did Mark initially add to the bowl?

##Solution## First, figure out how much punch was left in the bowl before Mark refilled it by subtracting the 12 gallons he added from the bowl's total capacity: 16 - 12 = <<16-12=4>>4 gallons Next, figure out how much punch was in the bowl before Sally came along: 4 + 2 = <<4+2=6>>6 gallons. Next, figure out how much punch was in the bowl before Mark started to refill it: 6 - 4 = <<6-4=2>>2 gallons Finally, multiply that amount by 2 to find out how much punch there was before the cousin drank half: 2 * 2 = <<4=4>>4 gallons #### 4

A sack of rice, which is 50 kilograms, costs $50. If David sells it for $1.20 per kilogram, how much will be his profit?

##Solution## David's revenue for the 50 kilograms of rice is $1.20 x 50 = $<<1.20*50=60>>60. So, his profit is $60 - $50 = $<<60-50=10>>10. #### 10

In the honey shop, the bulk price of honey is $5 per pound and the minimum spend is $40 before tax. The honey is taxed at $1 per pound. If Penny has paid $240 for honey, by how many pounds has Penny’s purchase exceed the minimum spend?

##Solution## Including tax, a pound of honey costs 5 + 1 = <<5+1=6>>6 dollars The minimum purchase equals 40 / 5 = <<40/5=8>>8 pounds of honey. Penny has bought 240 / 6 = <<240/6=40>>40 pounds of honey Penny has exceeded the minimum purchase by 40 - 8 = <<40-8=32>>32 pounds. #### 32

Lars owns a bakeshop. She can bake 10 loaves of bread within an hour and 30 baguettes every 2 hours. If she bakes 6 hours a day, how many breads does she makes?

##Solution## Lars can bake 10 x 6 = <<10*6=60>>60 loaves of bread every day. She can also bake 30 x 3 = <<30*3=90>>90 baguettes every day. Therefore the total bread she can bake is 60 + 90 = <<60+90=150>>150. #### 150

We harvested 405 kg of apples. 90 kg were used to make fruit juice and 60 kg were given to a restaurant. The rest was sold in 5 kg bags and their sale brought in $408. What was the selling price of one bag of apples?

##Solution## The weight of apples used for juice and given to the restaurant is 60 + 90 = <<60+90=150>>150 kg Thus 405 – 150 = 255kg worth of apples were sold in 5 kg bags. There were 255 / 5 = <<255/5=51>>51 bags sold. So each bag was sold for 408 / 51 = $<<408/51=8>>8 #### 8

In 5 years, Joey will be as old as Beth is now. If Joey is 9 now, how old was Joey when Beth was Joey's age now?

##Solution## Beth is 5+9=<<5+9=14>>14 now. Beth was 9 years old 14-9=<<14-9=5>>5 years ago. Joey was 9-5=<<9-5=4>>4. #### 4

Gerald had 20 toy cars. He donated 1/4 of his toy cars to an orphanage. How many toy cars does Gerald have left?

##Solution## Gerald gave away 20 x 1/4 = <<20*1/4=5>>5 of his toy cars. Therefore, he is left with 20 - 5 = <<20-5=15>>15 toy cars. #### 15

There are 28 students in a class. Two-sevenths of them were absent last Monday. How many students were present last Monday?

##Solution## 28 x 2/7 = <<28*2/7=8>>8 students were absent last Monday. So, 28 - 8 = <<28-8=20>>20 students were present last Monday. #### 20

A park has 50 benches with a capacity of 4 people each. On a Sunday afternoon, 80 people were sitting on the benches. What's the number of available spaces on the benches that other people can sit on before the carrying capacity of the benches is full?

##Solution## In the park, 50 benches with a capacity of four people each have a total capacity of 50*4 = <<50*4=200>>200 sitting spaces. If 80 people are already using spaces, the number of empty spaces is 200-80 =120 #### 120

Patricia and Geoffrey went fishing to feed their group of campers. They caught an eight-pound trout, six two-pound bass, and two twelve-pound salmon. If each person will eat two pounds of fish, how many campers can they feed?

##Solution## The bass weigh 6 * 2 = <<6*2=12>>12 pounds in all. The salmon weigh 2 * 12 = <<2*12=24>>24 pounds in all. The trout, bass, and salmon together weigh 8 + 12 + 24 = <<8+12+24=44>>44 pounds. Each camper will eat 2 pounds of fish, so Patricia and Jeffrey can feed 44 / 2 = <<44/2=22>>22 campers. #### 22

It takes 10 minutes to wash a car, 15 minutes to change oil, and 30 minutes to change a set of tires. If mike washes 9 cars, changes the oil on 6 cars, and changes two sets of tires how many hours did he work?

##Solution## He spent 10 minutes *9 cars = <<10*9=90>>90 minutes washing cars He spent another 15 minutes * 6 cars = <<15*6=90>>90 minutes changing oil. He spent 2 cars * 30 minutes = <<2*30=60>>60 minutes changing tires. He spent 90 minutes + 90 minutes + 60 minutes = <<90+90+60=240>>240 minutes working He spent 240 minutes / 60 minutes = <<240/60=4>>4 hours working #### 4

Woody wants to buy a games console that costs $282. Woody already has $42 and receives an allowance of $24 every week. How many weeks will it take him to save the money he needs for the game console?

##Solution## Woody needs to save another $282 - $42 = $<<282-42=240>>240 to be able to afford a games console It will take Woody $240 / $24/week = <<240/24=10>>10 weeks to save up enough money #### 10

Travis has 10000 apples, and he is planning to sell these apples in boxes. Fifty apples can fit in each box. If he sells each box of apples for $35, how much will he be able to take home?

##Solution## The total of boxes of apples is 10000 / 50 = <<10000/50=200>>200. Therefore the total amount he can take home is 200 x $35 = $<<200*35=7000>>7000. #### 7000

Bogan laid out 10 maggots for her pet beetle. The beetle only ate 1 and Bogan had to throw out the rest. Later that day, she tried feeding again and the beetle ate 3. If Bogan served 20 maggots in total, how many did she attempt to feed the beetle the second time?

##Solution## Bogan served a total of <<20=20>>20 maggots Bogan gave the beetles 10 maggots in the first feeding Bogan gave the beetles 20-10=<<20-10=10>>10 maggots in the second feeding #### 10

The largest room in Mrs. McAvoy's house is 45 feet wide and 30 feet long. The smallest room in that same house is 15 feet wide and 8 feet long. What is the difference in area between the largest room and the smallest room?

##Solution## The area of the largest room is 45 ft x 30 ft = <<45*30=1350>>1350 sq ft The area of the smallest room is 15 ft x 8 ft = <<15*8=120>>120 sq ft The difference between the two is 1350 sq ft - 120 sq ft = <<1350-120=1230>>1230 sq ft #### 1230

Michael and Thomas are selling their lego collections. They agree to split any money they earn. They sell them based on how many circles are on top. Each circle costs 1 cent. They earned $5 each after selling 100 single pieces, 45 double pieces, 50 triple pieces and a number of quadruple pieces. How many quadruple pieces did they sell?

##Solution## They made $10 because 2 x 5 = <<2*5=10>>10 They made $1 off single pieces because 100 x .01 = <<100*.01=1>>1 They made $.9 off double pieces because 45 x .02 = <<45*.02=.9>>.9 They made $1.5 off triple pieces because 50 x .03 = <<50*.03=1.5>>1.5 They earned $3.4 off the first three types because 1 + .9 + 1.5 = <<1+.9+1.5=3.4>>3.4 They earned $6.6 off the quadruple pieces because 10 - 3.4 = <<10-3.4=6.6>>6.6 They sold 165 quadruple pieces because 6.6 / .04 = <<6.6/.04=165>>165 #### 165

Logan makes $65,000 a year. He spends $20,000 on rent every year, $5000 on groceries every year, and $8000 on gas every year. If he wants to have at least $42000 left, how much more money must he make each year?

##Solution## Logan spends 20000+5000+8000 = <<20000+5000+8000=33000>>33000 a year. Logan has 65000-33000 = <<65000-33000=32000>>32000 left a year. Logan needs to make 42000-32000 = <<42000-32000=10000>>10000 more a year. #### 10,000

Of 96 oranges, half were ripe. If 1/4 of the ripe oranges were eaten and 1/8 of the unripe oranges were eaten, how many were left eaten in total?

##Solution## There were 96/2 = <<96/2=48>>48 ripe oranges. 48/4 = <<48/4=12>>12 ripe oranges were eaten. 48/8 = <<48/8=6>>6 unripe oranges were eaten. There were 12+6 = <<12+6=18>>18 oranges eaten in total. There were 96-18 = <<96-18=78>>78 oranges left uneaten. #### 78

Baking in batches of 65 cupcakes, Carla made 45 batches of cupcakes for her daughter's birthday party. She then took 5 cupcakes from each batch, and fed them to her dogs. If Carla's daughter had 19 friends and they shared the remaining cupcakes equally among them, including the daughter, calculate the number of cupcakes that each of Carla's daughter's friends ate.

##Solution## If Carla sampled 5 cupcakes from each batch and fed them to her dogs, each batch had 65-5 = 60 cupcakes afterwards. Since Carla made 45 batches of cupcakes for her daughter's birthday party, after removing the 5 cupcakes from each batch, Carla's daughter and her friends received 45*60 = <<45*60=2700>>2700 cupcakes. The total number of people at the party is 19 friends + 1 daughter = <<19+1=20>>20 After sharing the cupcakes equally among them, Carla's daughter and her friends each received 2700/20 = <<2700/20=135>>135 cupcakes #### 135

Randy drew 5 pictures. Peter drew 3 more pictures than Randy. Quincy drew 20 more pictures than Peter. How many pictures did they draw altogether?

##Solution## Peter drew 5+3 = <<5+3=8>>8 pictures. Quincy drew 20+8 = <<20+8=28>>28 pictures. Altogether they drew 5+8+28 = <<5+8+28=41>>41 pictures #### 41

Sally teaches elementary school and is given $320 to spend on books for her students. A reading book costs $12 and there are 30 students in her class. Unfortunately, if the money she is given by the school to pay for books is not sufficient, she will need to pay the rest out of pocket. How much money does Sally need to pay out of pocket, to buy every student a reading book?

##Solution## To purchase a book for each student, Sally needs: 30 x $12 = $<<30*12=360>>360. She thus needs to pay $360 - $320 = $<<360-320=40>>40 out of pocket. #### 40

Harry is 50 years old. His father is currently 24 years older than he is. How old was his mother when she gave birth to him if she is younger than his father by 1/25 of Harry's current age?

##Solution## Harry's father is 50 years + 24 years = <<50+24=74>>74 years old. Harry's mother is 1/25 * 50 years = <<1/25*50=2>>2 years younger than his father. So she is currently 74 years - 2 years = <<74-2=72>>72 years old. So when Harry was born, she was 72 years - 50 years = <<72-50=22>>22 years old. #### 22

Mark does a gig every other day for 2 weeks. For each gig, he plays 3 songs. 2 of the songs are 5 minutes long and the last song is twice that long. How many minutes did he play?

##Solution## He played 7*2 = <<7*2=14>>14 gigs The long song was 5*2=<<5*2=10>>10 minutes So all the gigs were 5+5+10=<<5+5+10=20>>20 minutes So he played 14*20=140 minutes #### 280

There were 50 people on the city bus. At the first stop, 15 people got off. At the next stop 8 people got off and 2 got on. At the third stop, 4 people got off and 3 people got on. How many people are on the bus after the third stop?

##Solution## The bus started with 50 people – 15 who got off at the first stop = <<50-15=35>>35 people on the bus. At the second stop, 35 people on the bus – 8 who got off = <<35-8=27>>27 people. Then there were 27 people + 2 who got on = <<27+2=29>>29 people on the bus. At the third stop, 29 people on the bus – 4 who got off = <<29-4=25>>25 people on the bus. Then there were 25 people on the bus + 3 who got on = <<25+3=28>>28 people on the bus. #### 28

In a certain school, 2/3 of the male students like to play basketball, but only 1/5 of the female students like to play basketball. What percent of the population of the school do not like to play basketball if the ratio of the male to female students is 3:2 and there are 1000 students?

##Solution## The students are divided into 3 + 2 = <<3+2=5>>5 parts where 3 parts are for males and 2 parts are for females. Each part represents 1000/5 = <<1000/5=200>>200 students. So, there are 3 x 200 = <<3*200=600>>600 males. And there are 2 x 200 = <<2*200=400>>400 females. Hence, 600 x 2/3 = 400 males play basketball. And 400 x 1/5 = <<400*1/5=80>>80 females play basketball. A total of 400 + 80 = <<400+80=480>>480 students play basketball. Therefore, 1000 - 480 = <<1000-480=520>>520 do not like to play basketball. The percentage of the school that do not like to play basketball is 520/1000 * 100 = <<520/1000*100=52>>52 #### 52

There are 15 cats in a shelter. One-third were adopted, and were replaced with twice the amount that were adopted. Later on, twice as many dogs showed up as there are cats. How many total animals are there in the shelter?

##Solution## 15/3=<<15/3=5>>5 cats were adopted out of 15 There were 15-5 = <<15-5=10>>10 cats left 5*2=<<5*2=10>>10 more cats were added. This makes 10+10=<<10+10=20>>20 cats in the shelter. 20*2=<<20*2=40>>40 dogs came into the shelter. There are now 20+40=<<20+40=60>>60 animals in the shelter. #### 60

A department store displays a 20% discount on all fixtures. What will be the new price of a 25 cm high bedside lamp that was worth $120?

##Solution## The amount of the discount is $120 x 0.2 = $<<120*0.2=24>>24. The new price will be $120 – $24 = $<<120-24=96>>96. #### 96

Mr. Rainwater has some goats, 9 cows and some chickens. He has 4 times as many goats as cows and 2 times as many goats as chickens. How many chickens does he have?

##Solution## Let X be the number of chickens Mr. Rainwater has. He has 4 goats/cow * 9 cows = <<4*9=36>>36 goats on his farm. So he has 36 goats / 2 goats/chicken = <<36/2=18>>18 chickens. #### 18

At camp Wonka, there are 96 campers. Two-thirds of the campers are boys, and the remaining one-third are girls. 50% of the boys want to toast marshmallows and 75% of the girls want to toast marshmallows. If each camper gets one marshmallow to toast, how many marshmallows do they need?

##Solution## The girls make up one-third of the campers, so there are 96 /3 = <<96/3=32>>32 girls. The boys make up two-thirds of the campers, so there are 32 + 32 = <<32+32=64>>64 boys. There are 32 x 75% = <<32*75*.01=24>>24 girls who want to toast marshmallows. There are 64 x 50% = <<64*50*.01=32>>32 boys who want to toast marshmallows. They need 24 + 32 = <<24+32=56>>56 marshmallows. #### 56

A factory decides to stop making cars and start making motorcycles instead. When it made cars, per month, it cost $100 for materials, they could make 4 cars, and they sold each car for $50. Now that they make motorcycles it costs $250 for materials, but they sell 8 of them for $50 each. How much more profit do they make per month selling motorcycles instead of cars?

##Solution## They sold $200 worth of cars each month because 4 x 50 = <<4*50=200>>200 They made $100 a month off cars because 200 - 100 = <<200-100=100>>100 They sold $400 worth of motorcycles each month because 8 x 50 = <<8*50=400>>400 They make $150 a month off motorcycles because 400 - 250 = <<400-250=150>>150 They make $50 more a month off motorcycles than cars because 150 - 100 = <<150-100=50>>50 #### 50

Gwen received a $900 bonus at work and decided to invest this money in the stock market. She spent one-third of her bonus on stock A, one-third on stock B, and the remaining one-third on stock C. After one year, stock A and stock B had doubled in value, while stock C had lost half of its value. At the end of the year, how much were Gwen's stocks worth, in dollars?

##Solution## One-third of her bonus was $900/3 = $<<900/3=300>>300. After one year, stock A doubled in value and was worth $300*2 = $<<300*2=600>>600. After one year, stock B doubled in value and was worth $300*2 = $<<300*2=600>>600. After one year, stock C had lost half its value and was worth $300/2 = $<<300/2=150>>150. Altogether, at the end of the year, Gwen's stocks were worth $600+$600+$150 = $<<600+600+150=1350>>1350 #### 1350

James and John combine their friends lists. James has 75 friends. John has 3 times as many friends as James. They share 25 friends. How many people are on the combined list?

##Solution## John has 75*3=<<75*3=225>>225 people on his friends list So that means there are 225+75=<<225+75=300>>300 people on the list So once you remove duplicates there are 300-25=<<300-25=275>>275 people #### 275

It takes Jennifer 20 minutes to groom each of her 2 long hair dachshunds. If she grooms her dogs every day, how many hours does she spend grooming her dogs in 30 days?

##Solution## She has 2 dogs and it takes 20 minutes to groom just 1 dog so it takes her 2*20 = <<2*20=40>>40 minutes per day to groom 2 dogs In 30 days, she will have spent 30*40 = <<30*40=1200>>1,200 minutes grooming her dogs There are 60 minutes in an hour so she spends 1200/60 = <<1200/60=20>>20 hours grooming her dogs #### 20

Jim decides to open up a bike shop. The most common repair he does is fixing bike tires. He charges $20 for this and it cost him $5 in parts. In one month Jim does 300 of these repairs. He also does 2 more complex repairs for $300 each and cost $50 in parts. He also sells $2000 profit worth of things from his retail shop. If rent and other fixed expense for the shop is $4000 a month how much profit did the shop make?

##Solution## From each tire repair, he made 20-5=$<<20-5=15>>15 profit So repairs made him a profit of 15*300=$<<15*300=4500>>4500 The two complex repairs each made him 300-50=$<<300-50=250>>250 profit So those added 250*2=$<<250*2=500>>500 So his total profit from everything was 4500+500+2000=$<<4500+500+2000=7000>>7000 So he made a profit of 7000-4000=$<<7000-4000=3000>>3000 #### 3000

Mary went to the store to buy fruit. Apples cost $1, oranges cost $2, and bananas cost $3. For every 5 fruits that customers buy, the store offers a $1 discount. Mary buys 5 apples, 3 oranges, and 2 bananas. How much will she pay?

##Solution## For 5 apples, Mary will pay 5*1= <<5*1=5>>5 dollars. For 3 oranges, she will pay 3*2= <<3*2=6>>6 dollars. For 2 bananas, she will pay 2*3 = <<2*3=6>>6 dollars. She bought 5+3+2=<<5+3+2=10>>10 fruits For 10 fruits, Mary gets a discount of 10/5 = <<10/5=2>>2 dollars. In total, the bill is 5 + 6 + 6 = <<5+6+6=17>>17 dollars. Subtracting the discount offered by the stores, Mary will pay 17 - 2 = <<17-2=15>>15 dollars. #### 15

Mark deposited $88 in a bank. Bryan deposited $40 less than five times as much as Mark. How much did Mark deposit in the bank?

##Solution## Five times the amount Mark deposited is $88 x 5 = $<<88*5=440>>440. So, Mark deposited $440 - $40 = $<<440-40=400>>400. #### 400

Polly and Gerald went for a fun afternoon riding mini race cars at the munchkin track, which is a one-quarter mile circular track. Polly managed to circle the track 12 times in one half hour, but Gerald's car was malfunctioning, and he only moved at an average speed half of what Polly did. What speed did Gerald's car average, in miles per hour?

##Solution## Polly circled the one-quarter mile track 12 times in 0.5 hours at a speed of 12/0.5=24 circuits of the track per hour. 24/4 = <<24/4=6>>6 miles per hour Gerald traveled at a speed half of what Polly traveled for an average speed of 6/2=<<6/2=3>>3 miles per hour. #### 3

Mathilda is determined to pay back the money she owes a friend so she decides to pay an initial installment of $125. If she still has 75% left to pay, how much did she owe originally?

##Solution## Percentage means per 100, so if she still owes 75%, she must have paid 100% - 75% = 25% of the original amount. 25% of the original amount = (25/100)*original amount = $125 Multiplying both sides by (100/25) gives: original amount = (100/25)*$125 = $<<(100/25)*125=500>>500 #### 500

A school is adding 5 rows of seats to the auditorium. Each row has 8 seats and each seat costs $30. A parent, being a seat manufacturer, offered a 10% discount on each group of 10 seats purchased. How much will the school pay for the new seats?

##Solution## Ten seats amount to $30 x 10 = $<<30*10=300>>300. So there is $300 x 10/100 = $<<300*10/100=30>>30 discount for each 10 seats purchased. Thus, the total cost for every 10 seats is $300 - $30 = $<<300-30=270>>270. The school is going to buy 5 x 8 = <<5*8=40>>40 seats. This means that the school is going to buy 40/10 = <<40/10=4>>4 sets of 10 seats. Therefore, the school will pay a total of $270 x 4 = $<<270*4=1080>>1080 for the new seats #### 1080

Christi saw twice as many black bears as white bears and 40 more brown bears than black bears in a national park. If the number of black bears in the park is 60, calculate the population of bears in the park.

##Solution## If there are 60 black bears in the park and 40 more brown bears than black bears, there are 60+40 = <<60+40=100>>100 brown bears. The number of black and brown bears in the park is 100+60 = <<100+60=160>>160 Twice the number of black bears as white bears means 60/2 = <<60/2=30>>30 white bears. The population of bears in the national park is 30+160 = <<30+160=190>>190 #### 190

Steve finds 100 gold bars while visiting Oregon. He wants to distribute his gold bars evenly to his 4 friends. If 20 gold bars were lost on the way back to San Diego, how many gold bars will each of his 4 friends get when he returns?

##Solution## He only has 100 - 20 = <<100-20=80>>80 gold bars after losing 20 of them. He then gives each of his friends 80 ÷ 4 = <<80/4=20>>20 gold bars. #### 20

An office has 90 workers. 2/3rds of them are men and the rest are women. The company hires 10 new employees and 100% of them are women. What is the total percentage of women in the company now?

##Solution## 1/3rd of the workers before the new hires were women because 1 - (2/3) = 1/3 There were 30 women working for the company before the new hires There are now 40 women working for the company because 30 + 10 = <<30+10=40>>40 There are 100 people working for the company because 90 + 10 = <<90+10=100>>100 The proportion of women working in the company is .4 because 40 / 100 = <<40/100=.4>>.4 The percentage of women working in the company is now 40 because .4 x 100 = <<.4*100=40>>40 #### 40

Hilary is shucking corn from ears that grew on her farm. She gets four ears of corn per stalk, and she has 108 stalks growing. Half the ears of corn have 500 kernels of corn and the other half have 100 more. How many kernels of corn does Hilary have to shuck?

##Solution## She has 108 * 4 = <<108*4=432>>432 ears of corn to shuck. She gets 500 kernels of corn from half the ears and 500 + 100 = <<500+100=600>>600 kernels from the other half. Half the number of ears of corn is 432 / 2 = <<432/2=216>>216 ears. Thus, Hilary has 216 * 500 + 216 * 600 = 108000 + 129600 = <<216*500+216*600=237600>>237600 kernels to shuck. #### 237600

James decides to bulk up. He weighs 120 kg and gains 20% of his body weight in muscle and 1 quarter that much in fat. How much does he weigh now?

##Solution## He gains 120*.2=<<120*.2=24>>24 kg in muscles So he gains 24/4=<<24/4=6>>6 kg of fat That means he gains a total of 24+6=<<24+6=30>>30 kg of bodyweight So his new body weight is 120+30=<<120+30=150>>150 kg #### 150

Janet pays $40/hour for 3 hours per week of clarinet lessons and $28/hour for 5 hours a week of piano lessons. How much more does she spend on piano lessons than clarinet lessons in a year?

##Solution## First find the total Janet spends on clarinet lessons per week: $40/hour * 3 hours/week = $<<40*3=120>>120/week Then find the total Janet spends on piano lessons per week: $28/hour * 5 hours/week = $<<28*5=140>>140/week Then subtract her weekly clarinet spending from her weekly piano spending to find the weekly difference: $140/week - $120/week = $<<140-120=20>>20/week Then multiply the weekly difference by the number of weeks in a year to find the annual difference: $20/week * 52 weeks/year = $<<20*52=1040>>1040/year #### 1040

Roy owns a refrigerated warehouse where he stores produce before selling it at the farmer’s market. The fruits and vegetables he stores are very sensitive to temperature, and he must keep them all cold or they will spoil. One day, the power went out and the air conditioner was turned off for three hours, during which time the temperature rose by 8 degrees per hour. If Roy gets the power back on, it will activate the air conditioner to lower the temperature at the rate of 4 degrees F per hour. What is the amount of time, in hours, it will take for the air conditioner to restore the warehouse to 43 degrees F?

##Solution## At a rate of 8 degrees per hour, in three hours the temperature rose by 3*8=<<3*8=24>>24 degrees. At a rate of 4 degrees per hour, the air conditioner can reduce the temperature 24 degrees in 24/4=6 hours. #### 6

Very early this morning, Elise left home in a cab headed for the hospital. Fortunately, the roads were clear, and the cab company only charged her a base price of $3, and $4 for every mile she traveled. If Elise paid a total of $23, how far is the hospital from her house?

##Solution## For the distance she traveled, Elise paid 23 - 3 = <<23-3=20>>20 dollars Since the cost per mile is $4, the distance from Elise’s house to the hospital is 20/4 = <<20/4=5>>5 miles. #### 5

Josh is saving up for a box of cookies. To raise the money, he is going to make bracelets and sell them. It costs $1 for supplies for each bracelet and he sells each one for $1.5. If he makes 12 bracelets and after buying the cookies still has $3, how much did the box of cookies cost?

##Solution## He makes $.5 profit on each bracelet because 1.5 - 1 = <<1.5-1=.5>>.5 He earns $6 because 12 x .5 = <<12*.5=6>>6 The cookies cost $3 because 6 - 3 = <<6-3=3>>3 #### 3

Colin can skip at six times the speed that Brandon can. Brandon can skip at one-third the speed that Tony can. And Tony can skip at twice the speed that Bruce can. At what speed, in miles per hour, can Colin skip if Bruce skips at 1 mile per hour?

##Solution## Tony can skip at twice the speed that Bruce can, for a speed of 1*2=<<1*2=2>>2 miles per hour. Brandon can skip at one-third the speed that Tony can, for a speed of 2*(1/3) = 2/3 miles per hour. Colin can skip at six times the speed that Brandon can, for a speed of (2/3*6=4 miles per hour). #### 4

Janet, a third grade teacher, is picking up the sack lunch order from a local deli for the field trip she is taking her class on. There are 35 children in her class, 5 volunteer chaperones, and herself. She she also ordered three additional sack lunches, just in case there was a problem. Each sack lunch costs $7. How much do all the lunches cost in total?

##Solution## Janet needs 35 lunches for the kids + 5 for the chaperones + 1 for herself + 3 extras = <<35+5+1+3=44>>44 lunches. Each lunch is $7, so lunch for the field trip costs $7 per lunch * 44 lunches = $<<7*44=308>>308 total #### 308

At 30, Anika is 4/3 the age of Maddie. What would be their average age in 15 years?

##Solution## If Anika is 30 now, in 15 years, she'll be 30+15=<<30+15=45>>45 years old. At 30, Anika is 4/3 the age of Maddie, meaning Maddie is 4/3*30=<<4/3*30=40>>40 years. In 15 years, Maddie will be 40+15=<<40+15=55>>55 years old. Their total age in 15 years will be 55+45=<<55+45=100>>100 Their average age in 15 years will be 100/2=<<100/2=50>>50 #### 50