The Coin Problem Quiz

1. Tarzan bought a pencil for Jane and received change for $3 and 20 coins, all nickels and quarters. How many of each kind are given?

6 nickels and 10 quarters

15 nickels and 10 quarters

5 nickels and 5 quarters

10 nickels and 10 quarters

Tarzan received change for $3 and 20 coins. Since all the coins are either nickels or quarters, we can set up a system of equations to represent the given information. Let's assume that Tarzan received x nickels and y quarters. The value of x nickels is 5x cents, and the value of y quarters is 25y cents. According to the given information, the total value of the coins is $3, which is equal to 300 cents. So, we can write the equation 5x + 25y = 300. Additionally, we know that the total number of coins is 20, so we can write another equation x + y = 20. By solving these two equations simultaneously, we find that x = 10 and y = 10. Therefore, Tarzan received 10 nickels and 10 quarters.

Explanation

Tarzan received change for $3 and 20 coins. Since all the coins are either nickels or quarters, we can set up a system of equations to represent the given information. Let's assume that Tarzan received x nickels and y quarters. The value of x nickels is 5x cents, and the value of y quarters is 25y cents. According to the given information, the total value of the coins is $3, which is equal to 300 cents. So, we can write the equation 5x + 25y = 300. Additionally, we know that the total number of coins is 20, so we can write another equation x + y = 20. By solving these two equations simultaneously, we find that x = 10 and y = 10. Therefore, Tarzan received 10 nickels and 10 quarters.

2. John has a total of 19 nickels and dimes worth $1.65. How many of each type of coin does he have?

5 nickels and 14 dimes

5 nickels and 10 dimes

5 nickels and 12 dimes

2 nickels and 14 dimes

John has a total of 19 coins, made up of nickels and dimes. Let's assume he has x nickels and y dimes.

The value of x nickels is 5x cents, and the value of y dimes is 10y cents.

According to the problem, the total value of all the coins is $1.65, which is equal to 165 cents.

So, we can write the equation: 5x + 10y = 165.

To find the values of x and y, we need to solve this equation.

By trial and error, we can see that when x = 5 and y = 14, the equation is satisfied.

Therefore, John has 5 nickels and 14 dimes.

Explanation

John has a total of 19 coins, made up of nickels and dimes. Let's assume he has x nickels and y dimes.

The value of x nickels is 5x cents, and the value of y dimes is 10y cents.

According to the problem, the total value of all the coins is $1.65, which is equal to 165 cents.

So, we can write the equation: 5x + 10y = 165.

To find the values of x and y, we need to solve this equation.

By trial and error, we can see that when x = 5 and y = 14, the equation is satisfied.

Therefore, John has 5 nickels and 14 dimes.

3. Paloma has quarters and nickels. She has twice as many quarters as nickels. If the value of the coins totals $4.40, how many quarters and nickels does Paloma have?

8 nickels and 16 quarters

4 nickels and 16 quarters

8 nickels and 10 quarters

18 nickels and 16 quarters

Let's assume that Paloma has x nickels. Since she has twice as many quarters as nickels, she would have 2x quarters. The value of each nickel is $0.05 and the value of each quarter is $0.25. The total value of the nickels would be 0.05x and the total value of the quarters would be 0.25(2x) = 0.50x. The total value of all the coins is $4.40, so we can set up the equation 0.05x + 0.50x = 4.40. Solving this equation, we find that x = 8. Therefore, Paloma has 8 nickels and 2(8) = 16 quarters.

Explanation

Let's assume that Paloma has x nickels. Since she has twice as many quarters as nickels, she would have 2x quarters. The value of each nickel is $0.05 and the value of each quarter is $0.25. The total value of the nickels would be 0.05x and the total value of the quarters would be 0.25(2x) = 0.50x. The total value of all the coins is $4.40, so we can set up the equation 0.05x + 0.50x = 4.40. Solving this equation, we find that x = 8. Therefore, Paloma has 8 nickels and 2(8) = 16 quarters.

4. Chantel has $4.85 in coins. If she has 6 more nickels than dimes and twice as many quarters as dimes, how many coins of each type does she have?

5

7

10

6

Chantel has 7 coins in total. Let's assume she has x dimes. Since she has 6 more nickels than dimes, she has x + 6 nickels. Also, she has twice as many quarters as dimes, so she has 2x quarters. The total value of the coins is $4.85. The value of the dimes is 0.10x, the value of the nickels is 0.05(x + 6), and the value of the quarters is 0.25(2x). Setting up the equation 0.10x + 0.05(x + 6) + 0.25(2x) = 4.85 and solving for x, we find that x = 7. Therefore, Chantel has 7 dimes, 13 nickels, and 14 quarters.

Explanation

Chantel has 7 coins in total. Let's assume she has x dimes. Since she has 6 more nickels than dimes, she has x + 6 nickels. Also, she has twice as many quarters as dimes, so she has 2x quarters. The total value of the coins is $4.85. The value of the dimes is 0.10x, the value of the nickels is 0.05(x + 6), and the value of the quarters is 0.25(2x). Setting up the equation 0.10x + 0.05(x + 6) + 0.25(2x) = 4.85 and solving for x, we find that x = 7. Therefore, Chantel has 7 dimes, 13 nickels, and 14 quarters.

5. Grandma saves all of her quarters and dimes in a jar. She collected 170 coins that are worth $26. How many of each coin does she have?

60 quarters and 110 dimes

40 quarters and 110 dimes

60 quarters and 100 dimes

50 quarters and 90 dimes

Grandma collected a total of 170 coins. Let's assume she has x quarters and y dimes.
Since a quarter is worth 25 cents and a dime is worth 10 cents, the total value of the quarters can be represented as 25x and the total value of the dimes can be represented as 10y.
According to the given information, the total value of all the coins is $26, so we can write the equation as 25x + 10y = 2600 (since 1 dollar = 100 cents).
To find the number of each coin, we need to solve this equation. The solution is x = 60 and y = 110, which means Grandma has 60 quarters and 110 dimes.

Explanation

Grandma collected a total of 170 coins. Let's assume she has x quarters and y dimes.
Since a quarter is worth 25 cents and a dime is worth 10 cents, the total value of the quarters can be represented as 25x and the total value of the dimes can be represented as 10y.
According to the given information, the total value of all the coins is $26, so we can write the equation as 25x + 10y = 2600 (since 1 dollar = 100 cents).
To find the number of each coin, we need to solve this equation. The solution is x = 60 and y = 110, which means Grandma has 60 quarters and 110 dimes.

6. Colin has $1.15 in his wallet, which contains 18 coins in nickels and dimes. Find how many of each kind coin he has in his wallet.

5 nickels and 5 dimes

13 nickels and 5 dimes

5 nickels and 115 dimes

13 nickels and 8 dimes

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Explanation

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7. In a collection of dimes and quarters there are 6 more dimes than quarters. If there is $29.65 overall, how many of each are there?

183 quarters and 89 dimes

83 quarters and 89 dimes

83 quarters and 189 dimes

3 quarters and 89 dimes

Let's assume the number of quarters is x. Since there are 6 more dimes than quarters, the number of dimes would be x+6.

The total value of quarters would be 0.25x, and the total value of dimes would be 0.10(x+6).

Given that the overall amount is $29.65, we can set up the equation 0.25x + 0.10(x+6) = 29.65.

By solving this equation, we find that x = 83. Therefore, there are 83 quarters and 89 dimes.

Explanation

Let's assume the number of quarters is x. Since there are 6 more dimes than quarters, the number of dimes would be x+6.

The total value of quarters would be 0.25x, and the total value of dimes would be 0.10(x+6).

Given that the overall amount is $29.65, we can set up the equation 0.25x + 0.10(x+6) = 29.65.

By solving this equation, we find that x = 83. Therefore, there are 83 quarters and 89 dimes.

8. Josh has 4 more quarters than dimes. If he has a total of $1.70, how many quarters and dimes does he have?

2

3

2.5

3.5

Let's assume the number of dimes Josh has is x. Since he has 4 more quarters than dimes, the number of quarters he has is x + 4. The value of x dimes is 10x cents, and the value of (x + 4) quarters is 25(x + 4) cents. The total value of his coins is $1.70, which is equal to 170 cents. Therefore, the equation can be formed as 10x + 25(x + 4) = 170. Solving this equation, we get x = 2. So, Josh has 2 dimes and 2 + 4 = 6 quarters.

Explanation

Let's assume the number of dimes Josh has is x. Since he has 4 more quarters than dimes, the number of quarters he has is x + 4. The value of x dimes is 10x cents, and the value of (x + 4) quarters is 25(x + 4) cents. The total value of his coins is $1.70, which is equal to 170 cents. Therefore, the equation can be formed as 10x + 25(x + 4) = 170. Solving this equation, we get x = 2. So, Josh has 2 dimes and 2 + 4 = 6 quarters.

9. Mom had $11.85 in her purse. She only had nickels and quarters in her purse. The number of quarters is equal to one less than twice the number of nickels. How many of each kind of coin did she have?

10 nickels and 43 quarters

20 nickels and 43 quarters

22 nickels and 43 quarters

22 nickels and 40 quarters

Let's assume the number of nickels is N and the number of quarters is Q. The value of N nickels is 0.05N and the value of Q quarters is 0.25Q. We can create two equations based on the given information: Q = 2N - 1 (the number of quarters is equal to one less than twice the number of nickels) and 0.05N + 0.25Q = 11.85 (the total value of the coins is $11.85). By substituting the value of Q from the first equation into the second equation, we get 0.05N + 0.25(2N - 1) = 11.85. Solving this equation, we find that N = 22 and Q = 43. Therefore, she had 22 nickels and 43 quarters.

Explanation

Let's assume the number of nickels is N and the number of quarters is Q. The value of N nickels is 0.05N and the value of Q quarters is 0.25Q. We can create two equations based on the given information: Q = 2N - 1 (the number of quarters is equal to one less than twice the number of nickels) and 0.05N + 0.25Q = 11.85 (the total value of the coins is $11.85). By substituting the value of Q from the first equation into the second equation, we get 0.05N + 0.25(2N - 1) = 11.85. Solving this equation, we find that N = 22 and Q = 43. Therefore, she had 22 nickels and 43 quarters.

10. Magalia received a money order worth $13. She received 10 more dimes than nickels, and 22 more quarters than dimes. How many coins of each did she receive?

5 nickels, 20 dimes, and 40 quarters.

20 dimes, and 42 quarters.

10 nickels, 20 dimes, and 42 quarters.

10 nickels, 20 dimes, and 2 quarters.

Magalia received 10 nickels, 20 dimes, and 42 quarters. The question states that she received 10 more dimes than nickels, so the number of dimes is 10 more than the number of nickels. Additionally, it states that she received 22 more quarters than dimes, so the number of quarters is 22 more than the number of dimes. Therefore, the number of nickels is 10, the number of dimes is 20, and the number of quarters is 42.

Explanation

Magalia received 10 nickels, 20 dimes, and 42 quarters. The question states that she received 10 more dimes than nickels, so the number of dimes is 10 more than the number of nickels. Additionally, it states that she received 22 more quarters than dimes, so the number of quarters is 22 more than the number of dimes. Therefore, the number of nickels is 10, the number of dimes is 20, and the number of quarters is 42.