Answer:
- 9 nickels
- 12 dimes
- 6 quarters
Step-by-step 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.
