A child has a bottle full of pennies, nickels, dimes, and quarters. There are twice as many quarters as pennies, four × as many nickels as pennies, and five × as many dimes as nickels. How many more dimes does the child have than quarters?

Rationale

A child has 18 times as many dimes as quarters.

Given the relationships between the quantities of each coin type described in the question, the number of dimes is eighteen times that of the quarters. This can be determined by following the chain of ratios—there are twice as many quarters as pennies, four times as many nickels as pennies, and five times as many dimes as nickels.

A (18 × as many) CORRECT

This is the correct answer. According to the ratios provided in the question, if we let the number of pennies be p, then there are 2p quarters, 4p nickels, and 20p dimes. Hence, the number of dimes is 18 times the number of quarters (20p vs. 2p).

B (5 × as many) YOUR ANSWER

This answer might be based on the incorrect assumption that the number of dimes is five times the number of quarters. However, the question states that the number of dimes is five times the number of nickels, not quarters.

C (20 × as many) YOUR ANSWER

This answer might be based on the incorrect assumption that the number of dimes is twenty times the number of pennies or quarters. However, the question states that the number of dimes is five times the number of nickels, which, in turn, is four times the number of pennies, hence making the total number of dimes 20 times the number of pennies and 10 times the number of quarters.

D (10 × as many) YOUR ANSWER

This answer might be based on the incorrect assumption that the number of dimes is ten times the number of quarters. However, the question states that the number of dimes is five times the number of nickels, which is four times the number of pennies, and the number of quarters is twice the number of pennies. Therefore, the number of dimes is 10 times the number of nickels and 18 times the number of quarters.

Conclusion

Given the ratios provided in the question, if we denote the number of pennies as p, then the number of quarters is 2p, nickels are 4p, and dimes are 20p. Therefore, the number of dimes is 18 times the number of quarters, not 5, 20, or 10 times as many. This demonstrates the importance of carefully reading and interpreting the information given in a problem.

A child has a bottle full of pennies, nickels, dimes, and quarters. There are twice as many quarters as pennies, four × as many nickels as pennies, and five × as many dimes as nickels. How many more dimes does the child have than quarters?

A child has 18 times as many dimes as quarters.

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