Question

A collection of coins consists of nickels, dimes, and quarters. There are

three fewer quarters than nickels and six more dimes than quarters. How
many of each kind of coin is in the collection if the total value of the
collection is $3.15?

Answer 1

• 9 nickels
• 12 dimes
• 6 quarters

Explanation:

We are given relations between the number of each kind of coin and the number of quarters. So, it is convenient to write an equation in terms of the number of quarters.

Let q represent the number of quarters. The number of nickels is 3 more than that, so is (q+3). The number of dimes is 6 more than the number of quarters, so is (q+6). The total value of the coins, in cents, is ...

5(q +3) +10(q +6) +25q = 315

40q +75 = 315 . . . . . . . . . . . . . . collect terms

40q = 240 . . . . . . . . . subtract 75

q = 6 . . . . . . . . . divide by 40

q +3 = 9 . . . . number of nickels

q +6 = 12 . . . number of dimes

There are 9 nickels, 12 dimes, and 6 quarters in the collection.