9514 1404 393
Answer:
- 20 dimes
- 8 quarters
- 2 half-dollars
Step-by-step explanation:
Let d, q, h represent the numbers of dimes, quarters, and halves Brian has. We can write 3 equations in these 3 variables:
10d +25q +50h = 500 . . . . value of the coins, in cents
d + q + h = 30 . . . . . . . . . . . total number of coins
4h = q . . . . . . . . . . . . . . . . . four times as many quarters as halves
Using the last equation to substitute into the other two, we get ...
10d + 150h = 500
d +5h = 30
The second equation can be written as ...
5h = 30 -d
and the first can be written to facilitate substitution:
10d +30(5h) = 500
10d +30(30-d) = 500 . . . . . substitute for 5h
900 -20d = 500 . . . . . . . . . simplify
400 = 20d . . . . . . . . . . . . . add 20d-500 to both sides
d = 20 . . . . . . . . . . . . . . . . divide by 20
Brian has 20 dimes.
