A coin bank contains some twenty-cent and fifty-cent coins in the ratio of 2 : 5.
When 10 fifty-cent coins are taken out and
exchanged with some twenty-cent coins of the same value,
the ratio became 9 : 8.
Find the sum of money in the coin box in dollars.

	Make p the same. (1) x 8 = (3)	(1) 20-cent	(2) 50-cent	Make p the same. (2) x 9 = (4)
Before	16 u	2 u	5 u	45 u
Change	+ 200	+ 25	- 10	- 90
After	72 p	9 p	8 p	72 p

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

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

2 u + 25 = 9 p --- (1)
5 u - 10 = 8 p --- (2)

Make p the same.

(1) _{x 8}
16 u + 200 = 72 p --- (3)

(2) _{x 9}
45 u - 90 = 72 p --- (4)

(4) = (3)
45 u - 90 = 16 u + 200
45 u - 16 u = 200 + 90
29 u = 290

1 u = 290 ÷ 29 = 10

Value of twenty-cent coins
= 2 u x 20
= 2 x 10 x 20
= 400¢

Value of fifty-cent coins
= 5 u x 50
= 5 x 10 x 50
= 2500¢

Total value of coins
= 400 + 2500
= 2900¢

100¢ = $1

Sum of money in the coin box
= 2900¢
= $29

Answer(s): $29