Question

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

Answer 1

• 18 dimes

Explanation:

Let the number of dimes be d and quarters be q

The value is $8.80 = 880¢, so:

• 10d + 25q = 880 ⇒ 2d + 5q = 176

If the dimes were quarters and the quarters were dimes, the coins' total value would be $7.30 or 730¢

• 25d + 10q = 730 ⇒ 5d + 2q = 146

Now we have 2 equations. Solving the system by elimination, subtract 5 times the second equation from twice the first equation:

• 2(2d + 5q) - 5(5d + 2q) = 2(176) - 5(146)
• 4d - 25d = -378
• -21d = -378
• d = -378/-21
• d = 18