A coin bank contains some ten-cent and fifty-cent coins in the ratio of 4 : 5.
When 20 fifty-cent coins are taken out and
exchanged with some ten-cent coins of the same value,
the ratio became 6 : 7.
Find the sum of money in the coin box in dollars.

	Make p the same. (1) x 7 = (3)	(1) 10-cent	(2) 50-cent	Make p the same. (2) x 6 = (4)
Before	28 u	4 u	5 u	30 u
Change	+ 700	+ 100	- 20	- 120
After	42 p	6 p	7 p	42 p

Value of 20 fifty-cent coins
= 20 x 50
= 1000¢

Number of ten-cent coins to exchange for
= 1000 ÷ 10
= 100

4 u + 100 = 6 p --- (1)
5 u - 20 = 7 p --- (2)

Make p the same.

(1) _{x 7}
28 u + 700 = 42 p --- (3)

(2) _{x 6}
30 u - 120 = 42 p --- (4)

(4) = (3)
30 u - 120 = 28 u + 700
30 u - 28 u = 700 + 120
2 u = 820

1 u = 820 ÷ 2 = 410

Value of ten-cent coins
= 4 u x 10
= 4 x 410 x 10
= 16400¢

Value of fifty-cent coins
= 5 u x 50
= 5 x 410 x 50
= 102500¢

Total value of coins
= 16400 + 102500
= 118900¢

100¢ = $1

Sum of money in the coin box
= 118900¢
= $1189

Answer(s): $1189