Question

A jar of coins contains dimes, pennies, nickels, and quarters. There are 32 nickels in the jar. The number of pennies is equal to the number of nickels plus the number of dimes. There are 3 quarters for every 4 nickels, and there are 2 dimes for every quarter. Which of the following is true?

A. There are 32 quarters and 24 dimes.
B. There are 80 pennies and 48 quarters.
C. There are 24 quarters and 48 pennies.
D. There are 48 dimes and 80 pennies.

Answer 1

To find the number of each type of coin in the jar, assign variables to represent each type of coin. Use the given information to set up equations and solve for the variables. The correct option is D, with 48 dimes and 80 pennies.

Step-by-step explanation:

To solve this problem, let's assign variables to represent the number of each type of coin.

Let's say 'd' represents the number of dimes, 'p' represents the number of pennies, 'n' represents the number of nickels, and 'q' represents the number of quarters.

From the given information, we know that there are 32 nickels in the jar, so n = 32.

The number of pennies is equal to the number of nickels plus the number of dimes, so p = n + d.

There are 3 quarters for every 4 nickels, so q = 3/4 * n = 3/4 * 32 = 24.

There are 2 dimes for every quarter, so d = 2 * q = 2 * 24 = 48.

Therefore, the correct option is D. There are 48 dimes and 80 pennies.