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

	Make p the same. (1) x 7 = (3)	(1) 20-cent	(2) 50-cent	Make p the same. (2) x 10 = (4)
Before	35 u	5 u	4 u	40 u
Change	+ 175	+ 25	- 10	- 100
After	70 p	10 p	7 p	70 p

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

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

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

Make p the same.

(1) _{x 7}
35 u + 175 = 70 p --- (3)

(2) _{x 10}
40 u - 100 = 70 p --- (4)

(4) = (3)
40 u - 100 = 35 u + 175
40 u - 35 u = 175 + 100
5 u = 275

1 u = 275 ÷ 5 = 55

Value of twenty-cent coins
= 5 u x 20
= 5 x 55 x 20
= 5500¢

Value of fifty-cent coins
= 4 u x 50
= 4 x 55 x 50
= 11000¢

Total value of coins
= 5500 + 11000
= 16500¢

100¢ = $1

Sum of money in the coin box
= 16500¢
= $165

Answer(s): $165