A coin bank contains some twenty-cent and fifty-cent coins in the ratio of 5 : 6.
When 20 fifty-cent coins are taken out and
exchanged with some twenty-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) 20-cent	(2) 50-cent	Make p the same. (2) x 7 = (4)
Before	40 u	5 u	6 u	42 u
Change	+ 400	+ 50	- 20	- 140
After	56 p	7 p	8 p	56 p

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

Number of twenty-cent coins to exchange for
= 1000 ÷ 20
= 50

5 u + 50 = 7 p --- (1)
6 u - 20 = 8 p --- (2)

Make p the same.

(1) _{x 8}
40 u + 400 = 56 p --- (3)

(2) _{x 7}
42 u - 140 = 56 p --- (4)

(4) = (3)
42 u - 140 = 40 u + 400
42 u - 40 u = 400 + 140
2 u = 540

1 u = 540 ÷ 2 = 270

Value of twenty-cent coins
= 5 u x 20
= 5 x 270 x 20
= 27000¢

Value of fifty-cent coins
= 6 u x 50
= 6 x 270 x 50
= 81000¢

Total value of coins
= 27000 + 81000
= 108000¢

100¢ = $1

Sum of money in the coin box
= 108000¢
= $1080

Answer(s): $1080