A coin bank contains some five-cent and twenty-cent coins in the ratio of 4 : 5.
When 5 twenty-cent coins are taken out and
exchanged with some five-cent coins of the same value,
the ratio became 7 : 8.
Find the sum of money in the coin box in dollars.

	Make p the same. (1) x 8 = (3)	(1) 5-cent	(2) 20-cent	Make p the same. (2) x 7 = (4)
Before	32 u	4 u	5 u	35 u
Change	+ 160	+ 20	- 5	- 35
After	56 p	7 p	8 p	56 p

Value of 5 twenty-cent coins
= 5 x 20
= 100¢

Number of five-cent coins to exchange for
= 100 ÷ 5
= 20

4 u + 20 = 7 p --- (1)
5 u - 5 = 8 p --- (2)

Make p the same.

(1) _{x 8}
32 u + 160 = 56 p --- (3)

(2) _{x 7}
35 u - 35 = 56 p --- (4)

(4) = (3)
35 u - 35 = 32 u + 160
35 u - 32 u = 160 + 35
3 u = 195

1 u = 195 ÷ 3 = 65

Value of five-cent coins
= 4 u x 5
= 4 x 65 x 5
= 1300¢

Value of twenty-cent coins
= 5 u x 20
= 5 x 65 x 20
= 6500¢

Total value of coins
= 1300 + 6500
= 7800¢

100¢ = $1

Sum of money in the coin box
= 7800¢
= $78

Answer(s): $78