A coin bank contains only quarters and dimes. The total value of the coins in the bank is $8.80. If the dimes were quarters and
the quarters were dimes, the coins' total value would be $7.30. Find the number of dimes in the bank
PLEASE EXPLAIN ANSWER
1 answer:
Answer:
Step-by-step explanation:
Let the number of dimes be d and quarters be q
<u>The value is $8.80 = 880¢, so:</u>
- 10d + 25q = 880 ⇒ 2d + 5q = 176
<u>If the dimes were quarters and the quarters were dimes, the coins' total value would be $7.30 or 730¢</u>
- 25d + 10q = 730 ⇒ 5d + 2q = 146
<u>Now we have 2 equations. Solving the system by elimination, subtract 5 times the second equation from twice the first equation:</u>
- 2(2d + 5q) - 5(5d + 2q) = 2(176) - 5(146)
- 4d - 25d = -378
- -21d = -378
- d = -378/-21
- d = 18
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