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english_AAAI_Math

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2a4b4cb16018411e860c36a08fa77b24

1

short_answer

January $$23$$, $$2019$$ can be written as $$8$$-digit date format $$23/01/2019$$. September $$2$$, $$2019$$ can be written as $$8$$-digit date format $$02/09/2019$$. How many digit "$$3$$" are there in all $$8$$-digit dates of the year $$2019$$?

adc0111f2b2c4d378ae08bcd6ee30b74

0

short_answer

Write down the number thirty three thousand and thirdy three in figures.

de32aa63739340c1b48d956920574cde

2

short_answer

A bakery sold durian, chocolate and strawberry puffs in the ratio of $$3:4:2$$. Each durian, chocolate and strawberry puff was sold for $$$5$$, $$$3$$, and $$$4$$. A total of $$$560$$ was collected on a Sunday afternoon. Find the amount of money collected from the sale of durian puffs.

9ec93e5371534d979ad30c4708659ad9

1

short_answer

$$A, B, C$$ and $$D$$ live in the same block of apartment that has $$18$$ level. Their name are Zachary, Yvonne, Xavier and Waylon. We know that: (1) $$A$$ stays in an unit that located higher than $$C$$, but lower than $$D$$ (2) $$B$$ stays in an unit that is lower than Xavier\textquotesingle s unit (3) $$D$$ stays in an unit that is $$5$$ times Yvonne\textquotesingle s unit (4) If Zachary moves to two level above his unit, the difference in level between his unit and Xavier\textquotesingle s unit is equal to the difference of his unit with Waylon\textquotesingle s unit. (5) The level that Zachary stays is the sum of the level Yvonne and Xavier stay. Based on the information above, do you know who is which level does $$A$$ stays in?

bbf5395114fa4ebba02cabdc25eef45a

1

short_answer

The surface of a $$7\times5\times14$$ cuboid is painted yellow. The cuboid is cut into $$490$$ small cubes of the same size. How many small cubes have exactly three faces that are painted yellow?

92b5600f34c745cc9d5dd15bf5842acc

1

short_answer

Chen writes down a two digit number. He finds that if he swaps the digits of the number round, the new number he creates is three more than one third of the original number. What was the \textbf{original} number?

64b747db943b470e8d5bcc4cd037f8bc

2

short_answer

Terence invested $10,000$ dollars in an investment that pays $6 \%$ interest compounded yearly for the first three years, and then $8 \%$ interest compounded yearly for the last two years. How much will he get when the investment is due? ($1.06^{3} \approx 1.191$ and $1.08^{2} \approx1.166$, round the result to the nearest hundredth)

97e7c5c45535473c925714e02efb350b

1

short_answer

$$5$$ raisin rolls and $$6$$ donuts cost ＄$$14.70$$. Each raisin roll costs $$3$$ times as much as each donut. How much is a raisin roll?

a72c43c3bde841a3810fb516a1d277f4

1

short_answer

Students from three different schools gather together to participate in a sports day. There are $24$, $36$, and $42$ students from the three schools, respectively. They are going to be divided into teams with equal numbers of students. The students of each team should come from the same school, and students from each school should be exactly divided into teams with no remainder. Find the largest possible number of students in each team.

beed278a1bed4c50a92eafa931245d88

1

short_answer

$200$-$100$ $\div$ $5$ +$200$

c0de10f834e9467fb65b332409f0b795

0

short_answer

Angel bought $3$ notebooks, $4$ pencil cases and $5$ erasers at $$$50$$. A notebook and a pencil case cost $$$6$$. A pencil case and an eraser cost $$$9$$. How much did a pencil case cost?

d16475774e2d40e298ca4d00de004671

2

short_answer

There is an arithmetic sequence. The sum of first $9$ terms is $99$. The sum of first $27$ terms is $540$. What is the sum of first $16$ terms?

907abf99743b45bcb21f5e10053628da

2

short_answer

A $$3$$-digit integer is called a \textquotesingle D-number\textquotesingle{} if the hundreds digit is divisible by both tens digit and the units digit. For example, $931$ is a \textquotesingle D-number\textquotesingle{} because $9$ is divisible by $3$ and $1$. How many $$3$$-digit \textquotesingle D-numbers\textquotesingle~are there?

e70904d7218642df8d9ac82e9cbb1818

2

short_answer

Julia writes a number sequence: $1, 2, 2, 3, 3, 3, 4, 4, 4, 4, 5\cdots $ According to the pattern, what is the median of all the numbers in the sequence when she finishes writting all the $12$s?

f026bb192f0f4088a86ad13d7cc26d86

1

short_answer

Using the digits $$4$$, $$5$$, and $$8$$, we can form~\uline{~~~~~~~~~~}~different numbers without repeating digits.

9626ae3648b54685b675bed33b248975

1

short_answer

Katie the baker can make $6$ loafs of bread with every $5$ cups of flour. How many cups of flour does Katie need to make $24$ loafs of bread?

2989d3782ec842dcb36b4a949d8588db

1

short_answer

There are 216 people at a camp. 139 of them are teachers and the rest of them are children. How many children are there?

d26a5497d6514135ba9d0ea0f54b8bb4

1

short_answer

How many digits are there from $$7$$ to $$40$$?~\uline{~~~~~~~~~~}~. $$7$$，$$8$$，$$9$$，$$10$$，\ldots\ldots，$$38$$，$$39$$，$$40$$

d495a6229050459d9704caa6c86a306f

2

short_answer

The $$2018$$ Russia World Cup is the $$21^{\rm st}$$ FIFA World Cup. There are $$32$$ teams competing for the championship. The $$2018$$ Russia World Cup includes two stages, the group stage and the knockout round. At the group stage, the $$32$$ teams are divided into $$8$$ groups and a single round-robin tournament is run within each group of $$4$$ teams. After the group stage, two winning teams are picked from each group of $$4$$ teams to advance to the knockout round, where the single elimination rule prevails for the win or loss of two teams in the World Cup, and the top $$8$$, top $$4$$, top $$2$$, the winner, the runner-up, the third place and the fourth place are produced. How many games are played throughout the $$2018$$ Russia World Cup?

26c05d1067be4f228420a8d03d60d1f1

1

short_answer

A red light flashes four times a minute and a green light flashes six times a minute. If both lights start flashing at the same instant, how many times do they flash at the same instant in one hour including the first and the last time?

bd83c15a08c149f196a2f6caf1bec626

2

short_answer

I\textquotesingle m thinking of a number. I triple it, then add $1$ and get an answer of $22$. What is the number I am thinking of?

b89d2244ef89497f80cc165487752747

2

short_answer

A gallery has a collection of $$120$$ paintings, some of which are by French artists. $$40 \%$$ of the paintings are landscapes; the rest are still lifes. Of the landscapes, $$25$$ paintings are by French artists. In total there are $$40$$ paintings by French artists. How many still lifes are there by artists who are~\textbf{not~}French? Answer:~\uline{~~~~~~~~~~}~

8a316589158f4d3da421f3970c3ae486

1

short_answer

Anita mixed $60$ml of rose syrup with $780$ml of water to make some rose drink. She poured the drink equally into $9$ glasses and had some rose drink left. Find the greatest volume of drink in each glass.

dc48d7be2274447aa61b412cef4e1d7b

1

short_answer

Amy mixed $$100$$ pounds of dogfood that is $$50 \%$$ rice with $$400$$ pounds of dogfood that is $$80 \%$$ rice. Find the concentration of rice in the new mixture.

c347b5871cff46138c8d8bcabd9edb4d

1

short_answer

Jasmin can ride a bike at a constant speed of $24$ meters per minute. How many meters can she ride in $300$ seconds?

93719c34b1574999936ad00f94cad2e8

1

short_answer

What is $$30.03-3.3$$? ANSWER~\uline{~~~~~~~~~~}~

25e1b3f1ea544f5fb040500722f553f5

2

short_answer

If $$S=2+22+222+2222+\cdots +\underbrace{222\cdots 222}_{2017 ; 2s}$$, what is the sum of the last $$5$$ digits of $$S$$?

e847f4218f9d4d7db291515e8c3a7f1e

1

short_answer

A pile of hay can feed $$12$$ horses for $$15$$ days. For how long could the same pile of hay feed $$20$$ horses?

8f71ad4877d946aca5623bd2c5a1ffd9

1

short_answer

Alice\textquotesingle s house number is a $$4$$-digit number. When she moves the first digit to the ones place, she notices that the new $$4$$-digit number is bigger than her house number by $$4707$$. What is her house number?

7181abe12a9441efa29c9b6450170e13

1

short_answer

Oliver is $$20$$ this year, and Lin is $$26$$ this year, so how many years later will the sum of their ages be $$48$$?

4c625760244c484b9b010ff513d7aacb

0

short_answer

Work out $$6.67+5.93$$. ~\uline{~~~~~~~~~~}~

e8ea378d2e224df88c51e8df519dd96a

1

short_answer

Which of the following numbers is the closet to one? $0.0099$, $0.81$, $1.2$, $0.087$, $1.21$

41c299f84c8e465ab37555ce3abe8dbd

1

short_answer

Sandra is $$8$$ years old and her mother is $$4$$ times her age. What was the difference in their ages $2$ years ago?

44be0754c9694d719af9a93c29de6a7f

2

short_answer

Find the smallest multiple of $$35$$ that ends with the two-digit \textquotesingle$$35$$\textquotesingle{} where the sum of all its digits is $$35$$.

af1991b7f84d4f62aaf6b6878cddfe02

2

short_answer

Mrs Lim spent ＄$$4y$$ on a watch and ＄$$20$$ on a handbag. She gave the remainder of her money to her $$2$$ children. Each child received ＄$$ \left( {y-5} \right) $$. Suppose that she had $8y$ at first, find the value of $y$.

42c5c84cc6f5475fbadec4fb054ea542

1

short_answer

Leap years have $$366$$ days; all other years have $$365$$ days. Each $$4$$th year ($$1904$$, $$1908$$, $$1912$$, and so on) was a leap year. Britain celebrated the start of the $$20$$th Century on $$1$$st January $$1901$$ and the start of the new Millennium on $$1$$st January $$2000$$ , $$99$$ years later. Calculate the number of days from one date to the other inclusive.

99f53a3e706d464e97e730165f364f49

1

short_answer

Andy had £100 pocket money. He deposits £10 on the first day, spends £8 on the second day, deposits £10 on the third day, spends £8 on the fourth day, and so on. How much money does he have in 15 days?

d079d30d875545e8b201477ce3c16428

2

short_answer

How many numbers that are less than $$100$$ cannot be divided exactly by $$3$$ or $$7$$?

f0ef1fefe9e4405cb773c5fc47ab6e50

1

short_answer

$5.6{\rm{ }} \times {\rm{ }}2.4$

c4423db7405342c1aecbf4c4b4097957

0

short_answer

Find the Highest Common Factor of the following pair of numbers $$16$$ and $$28$$.

0ddcfdef95d9497987f43afbe170f9f1

1

short_answer

Each hour a grandfather clock strikes the number of hours. How many strikes would there be in $$12$$ hours? ~\uline{~~~~~~~~~~}~

b92d0cd587064c7195d1d5818981c69c

2

short_answer

A ten-pence coin weighs $2\dfrac{1}{2}$g. I have 40 pence worth of ten-pence coins. How much does this weigh?

0e1b4fc3bb9a4b798f86eca17838ecba

2

short_answer

The total number of buttons that James and Nina have is $22$. Nina has more buttons than James. When Nina gave $4$ of her buttons to James, then they have the same number of buttons. How many buttons does Nina have originally?

83396f638262415bb8e62a96478ffa20

1

short_answer

The total cost of a mango and a pear was £3.40. The total cost of a mango and an apple was £3.80. Brad bought 4 mangoes, 2 pears and an apple for £13.20. Find the cost of a mango.

fc18df7e18e04a7ba182dc1493c19ef1

1

short_answer

There were $$6$$ questions in a mathematics competition. $$5$$ marks would be awarded for every correct answer. $$2$$ marks would be deducted for a wrong answer. If Valerie scored $$23$$ marks in the mathematics competition, how many questions did she answer correctly?

2035192c81ab4e4ca4f6708f47f4638d

1

short_answer

There were $20$ people on a bus. The ratio of the number of adults to the number of children was $1:4$. How many adults were there?

f83ac99f77f44f1eb0edef1268dfc574

3

short_answer

A box is projected up a long ramp (incline angle with the horizontal = 37°) with an initial speed of 10 m/s. If the surface of the ramp is very smooth (essentially frictionless), how high up the ramp will the box go? What distance along the ramp will it slide?

2628cccb1cfe4903b268f7641a4ef75c

1

short_answer

Mr Chan wants to give $$35$$ candies to $$9$$ children with seat number $$1$$ to $$9$$ in order. Each child will receive $$1$$ candy each time. Teacher Mr Chan gives the first candy to the child on seat number $$3$$. Which child will receive the last candy?

21305df1a3f34c78b15a5895829b6b0e

1

short_answer

A tennis racket and $$3$$ identical tennis balls have a total mass of $$536\rm g$$. $$2$$ such tennis rackets and $$3$$ such tennis balls have a total mass of $$904\rm g$$. What is the mass of a tennis racket?

13b8f82b60e940e09ee1f5cec6149d01

1

short_answer

What is the sum of the following numbers? 9 + 12 + 17 + 18 + 21 + 23 =

8570bae0d8974f76bc97044f422b89b5

1

short_answer

There are $$5$$ blue balls, $$4$$ orange balls and $$2$$ yellow balls in a bag. Sheila will be blindfolded before she takes the balls out, one at a time. How many balls must Sheila take out in order to get $$2$$ groups of $$4$$ balls of the same colour?

e884adb0e6b040cdb2a34a42819fab4c

2

short_answer

Calculate $30 + 30 \times 30 + 30 \times 30 \times 30$

0dbf1ccfd2fc4007a533a919605fe57f

1

short_answer

There are $$64$$ players taking part in a knock-out quiz tournament. Each match in the tournament involves $$4$$ players. Only the winner of the match remains in the tournament and the other three players are knocked out. How many matches are required until there is an overall winner?

2473e761fb61498e9259082d612f70e0

1

short_answer

$2.5\times24$

17e5719cf1f44333aa04f4722862715a

1

short_answer

Calculate: $$782-9\times 24\div 2$$ $ $ $ $ $ $ $ $ $ $

ae73ec11506148a9bdc9da9a59f4f805

0

short_answer

What is the sum of the following numbers? $$1+3+5+95+97+99=$$

4109885176844bd28d5df4cb978b2199

1

short_answer

Alice\textquotesingle s house number is a $$4$$-digit number. When she moves the first digit to the ones place, she notices that the new $$4$$-digit number is bigger than her house number by $$4707$$. What is her house number?

328cb846f149403d8585071dd7244539

1

short_answer

A piece of cheese and 4 bags of flour weigh 22 kg in total. If a piece of cheese weighs 6 kg, how much does a bag of flour weigh?

a3f26b4b45934be08cf8676828e7ba57

2

short_answer

There is an arithmetic sequence. The sum of first 9 terms is 72, and the the sum of first 23 terms is 736. What is the sum of first 16 terms?

3ae9a5c1a17b4f1095105ce89b2df771

0

short_answer

A CD in England costs £$14$ If Richard spent this amount of money in St Petersburg how many CDs could he buy?

50bc0ad9cea747f5b927172f53d8747a

2

short_answer

When it was his birthday, my uncle Isaac told me: ``$3$ years ago, my age was a square number. Next year it will be a prime number and in $12$ years\textquotesingle{} time, it will be a cube number." How old is lsaac? Circle the correct age: $28 39 52 84$

e8608d6fe45347b7a5f73ee97e718fe9

1

short_answer

Multiply $$168$$ by $$91$$.~\uline{~~~~~~~~~~}~

34b8599fcad846d6b22ce1cb7e0d67e3

2

short_answer

Bart has an M\&M\textquotesingle s chocolate pack with $3$ red M\&M\textquotesingle s chips, $4$ yellow M\&M\textquotesingle s chips and $5$ brown M\&M\textquotesingle s chips. Bart wants to get $2$ M\&M\textquotesingle s chips of different colours without looking. What is the smallest number of M\&M\textquotesingle s chips he needs to take out to make sure that he gets what he wants?

bc530cd877f2428bb79ffc956252f9b3

1

short_answer

Andrew, Bernice and Cassandra are climbing stairs from level $$1$$ with each of the climb at different speed. When Andrew reached level $$5$$, Bernice was at level $$3$$. When Bernice reached level $$6$$, Cassandra was already at level $$10$$. So, when Cassandra reached level $$19$$, which level will Andrew be at?

ee25df77dbc84b5194bfbcc0c0bd215c

1

short_answer

Given $$\vee $$ defines a new operation such that $$a\vee b=a\times b+a+b$$, and if $$2\vee \left( x\vee 4 \right)=59$$, what is $$x$$?

751fb35fe9d44a4db9f500a8a4b466c9

1

short_answer

The pattern $$234523452345\ldots{} $$ is continued to form a $$43$$-digit number. What is the sum of all $$43$$ digits?

a7221d21ffb140cf886d39364cd7c81f

1

short_answer

$43242 \div 100$

43310de103274061a3f319f61ec706e8

1

short_answer

James takes $$30$$ minutes to finish a $$6$$ question math quiz. How many hours does James need to take $$4$$ quiz in total?

0ace0cd817cf47d78db91f0ee0283a12

1

short_answer

How many centimetres are there in $4.7$ kilometres?

8e72117b5da04fdfb91ab3f9a9aab2cd

1

short_answer

Two drivers, Shafur and Samuel left Town $$X$$ for Town $$Y$$ at the same time. They drove at an average speed of $$54 \text {km/h}$$ and $$66 \text {km/h}$$ respectively. After they drove for $$40$$ minutes, Samuel decided to turn back to Town $$X$$ to refill the petrol while Shafur continued driving at the same speed. They reached Town $$Y$$ at the same time. Find the distance between Town $$X$$ and Town $$Y$$. (Assuming the time taken to refill the petrol was negligible)

a44dbd04ca324e2dade754b21d81088b

2

short_answer

Grandpa is 61 years old this year. His 3 grandsons are aged 4, 7 and 12. In how many years will the sum of the 3 grandsons be equal to their grandpa?

84c4b5d7849c464193a6bad9277ea2b6

1

short_answer

Mr Cohen bought $$4$$ identical tables and $$9$$ identical chairs for ＄$$504$$. The cost of each table was the total cost of $$3$$ such chairs. What was the cost of each chair?

260fe91f8f7f438498be6c9fceaafc9b

1

short_answer

How many different ways can you make $$40$$p with $$5$$p\textquotesingle s and $$10$$p\textquotesingle s?

b30c16550e45492986ba4327f062d606

1

short_answer

The first term of a sequence is $$50$$, the second is $$46$$ and the third is $$42$$, and so on. How many terms are there until the first negative term? ANSWER~\uline{~~~~~~~~~~}~

95bcebc21d174c318350f0c2fd3955a3

1

short_answer

Divide $100$ by $40$, leaving your answer as a decimal.

212dddf2d58c488f92051cac02b24a4d

1

short_answer

Find the smallest $$3$$-digit number such that the product of all its digits is also a $$3$$-digit number.

740a0eb88157475a86714273b6c58967

1

short_answer

Tina is arranging $$68$$ flowers into vases. If each vase can only hold $$9$$ flowers, at least how many vases are needed to hold all the flowers？

6a83a12baea34666bb5d5db02ee98315

1

short_answer

In the morning, the fruit market buys $$416$$ pounds of fruit, and the fruit market buys $$248$$ pounds of fruit in the afternoon. How many pounds of fruit does the fruit market buy in the morning than in the afternoon?

b216c4dcef5246b1a1032e1ce7b59830

1

short_answer

Without using a calculator, evaluate the following expressions. $\frac{7\div -3.\dot{3}}{\sqrt[3]{-0.027}}+\frac{2^{3}\div4^{2}}{0.125\times[1.8-(0.2\times7)]}-[\frac{0.1}{0.\dot{1}\dot{4}\dot{2}\dot{8}\dot{5}\dot{7}}+(2\times0.3)]=$~\uline{~~~~~~~~~~}~

ef74f31cad3e47e99a0e8f28fe1357b7

1

short_answer

How many multiples of $$3$$ are there from $$38$$ to $$81$$?

dda1e4bf25b443da8efc70aaf2624bc4

1

short_answer

What is the smallest number which is a multiple of $$12$$ and $$15$$?

8eceffc0fa6b407998bd0ae271a1ef01

1

short_answer

The following string of pyramid numbers has missed two angles, so how to do the calculation? $$3+4+5+6+\cdots +10+\cdots +6+5+4+3$$

7b05e8856130431fa24c3121679e2bb7

1

short_answer

Pip and Bud each have some pocket money. Pip has ￡$50$ more than Bud. When Pip has spent $80 \%$ of his pocket money and Bud has spent $\frac34$ of her pocket money, the ratio of Pip\textquotesingle s leftover pocket money to that of Bud is $6:5$. How much pocket money did Pip have to begin with?

0f28dcf2c6ad4abeb816c16558e621eb

1

short_answer

A phone shop sold $$22$$ more than half of their mobile phones in January. They sold $$13$$ more than half of the remaining mobile phones in February. They had $$78$$ mobile phones left. How many mobile phones did the shop carry at first?

8601fccdea1547d8bdbea5b58f76c291

1

short_answer

If $$\frac{3}{7}$$ of a number is $$18$$, what is $$\frac{5}{6}$$ of the \textbf{\uline{same}} number?

3a1798bad2d541fcb5c6a144f4ce03cd

1

short_answer

$5$ people play in a knockout tournament. How many games will be played to determine the winner?

297e8fe4a3fd48839219bc3a9649f928

1

short_answer

Mrs Raj bought $$50$$ more pens than pencils. She bought $$438$$ pens and pencils altogether. How many pencils did she buy?

9d2c6f4e1357450eaed4a31c6237f2d2

2

short_answer

Justin spent an average of $500$ dollars per month from January to April, $300$ dollars per month from May to July, $400$ dollars in total from August to September, and $300$ dollars per month from October to December. How much did he spent in average per month from January to December?

eeedd7f61d3f499e91214241749f7193

1

short_answer

Pip has 5 boxes of apples. Each box has 9 apples. He then gets 16 apples from Bud. How many apples does he have now?

4d8c3d77b070434f8e98c669130876ad

1

short_answer

Mrs Koh was preparing to give her four grandchildren red packets for Chinese New Year. She wanted to put $$$70$$ into each of the four red packets but realised that she would be short of $$$15$$. How much money did Mrs Koh have?

24ae47ec3af142b6a27136a41410c388

1

short_answer

Watson wrote down a number sequence: $$4$$，$$5$$，$$6$$，$$\cdots \cdots $$, $$49$$，$$50$$，$$51$$ The digit "$3$" in the number "$23$"~is the~\uline{~~~~~~~~~~}~digit he wrote.

252c59d9b9aa4aa9b64d371d39a82574

1

short_answer

5 people play a one-on-one knockout tournament. How many games will be played to determine the winner?

33067bcb25344c1d903a52e71d15db47

2

short_answer

Anna, Betsy and Chariene had a tolal of $$168$$ marbles. Charlano gave $$15$$ marbles to Betsy. Then, Batsy gave $$8$$ marbles to Anna. In tho end, tho ratio of the number of marbles that Anna had to the numbor of marblas that Betsy had to the number of marbles that Charlene had is $$2:5:7$$. How many marbles did Betsy have at first?

51a7705457af49c88147499591a76612

0

short_answer

Calculate the sum below. $$19 + 6 + 12 + 13 + 21 + 4 + 8 + 17$$

1383ca4e525041c99d8fa68660917e37

1

short_answer

Sara is looking for a book in the library. The librarian tells her, "all the shelves in our library are arranged in one row. The book you are looking for is located on the $$8$$\textsuperscript{th} shelf if you count from front to back, and the $$10$$\textsuperscript{th} if you count from back to front. " How many shelves are there in the library?

399908c2f1ad4ee9a7c420afd356fe12

2

short_answer

（AMC 2016 Question \#30） Mary has four children of different ages, all under 10, and the product of their ages is 2016. What is the sum of their ages?

1576b6692de34a408952ede9da9ad5ba

1

short_answer

Students are standing in a rectangular field. Chris is $7$\textsuperscript{th} in line counting from the front, and $4$\textsuperscript{th} in line counting from the back. He is also $3$\textsuperscript{rd}~in line counting from the left, and $7$\textsuperscript{th}~in line counting from the right. There are~\uline{~~~~~~~~~~}~students in total in the rectangular field.

22303a6e166b42b9a7f52651f42185f7

1

short_answer

Four years ago the combined age of 2 dogs was 10 years old. What will the combined age be in 2 years?

06699a3607d9471db8f9ba87968896ad

1

short_answer

Calculate: $$3.5\times \frac{4}{5}+5.5\times 80 \%+0.8 = $$

f58334bfc17f4a5ba758430811171cb6

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short_answer

In a bag of money to take to the bank I have only $$5\text{p}$$, $$10\text{p}$$ and $$20\text{p}$$ coins. I have twice as many $$20\text{p}$$ coins as $$10\text{p}$$ coins and half as many $$5\text{p}$$ coins as $$10\text{p}$$ coins. If the bag contains £$$15.75$$, haw many $$20\text{p}$$ coins are there?