A coin bank contains some twenty-cent and fifty-cent coins in the ratio of 4 : 5.
When 10 fifty-cent coins are taken out and
exchanged with some twenty-cent coins of the same value,
the ratio became 7 : 6.
Find the sum of money in the coin box in dollars.

	Make p the same. (1) x 6 = (3)	(1) 20-cent	(2) 50-cent	Make p the same. (2) x 7 = (4)
Before	24 u	4 u	5 u	35 u
Change	+ 150	+ 25	- 10	- 70
After	42 p	7 p	6 p	42 p

Value of 10 fifty-cent coins
= 10 x 50
= 500¢

Number of twenty-cent coins to exchange for
= 500 ÷ 20
= 25

4 u + 25 = 7 p --- (1)
5 u - 10 = 6 p --- (2)

Make p the same.

(1) _{x 6}
24 u + 150 = 42 p --- (3)

(2) _{x 7}
35 u - 70 = 42 p --- (4)

(4) = (3)
35 u - 70 = 24 u + 150
35 u - 24 u = 150 + 70
11 u = 220

1 u = 220 ÷ 11 = 20

Value of twenty-cent coins
= 4 u x 20
= 4 x 20 x 20
= 1600¢

Value of fifty-cent coins
= 5 u x 50
= 5 x 20 x 50
= 5000¢

Total value of coins
= 1600 + 5000
= 6600¢

100¢ = $1

Sum of money in the coin box
= 6600¢
= $66

Answer(s): $66