A coin bank contains some ten-cent and fifty-cent coins in the ratio of 3 : 8.
When 10 fifty-cent coins are taken out and
exchanged with some ten-cent coins of the same value,
the ratio became 8 : 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 8 = (4)
Before	21 u	3 u	8 u	64 u
Change	+ 350	+ 50	- 10	- 80
After	56 p	8 p	7 p	56 p

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

Number of ten-cent coins to exchange for
= 500 ÷ 10
= 50

3 u + 50 = 8 p --- (1)
8 u - 10 = 7 p --- (2)

Make p the same.

(1) _{x 7}
21 u + 350 = 56 p --- (3)

(2) _{x 8}
64 u - 80 = 56 p --- (4)

(4) = (3)
64 u - 80 = 21 u + 350
64 u - 21 u = 350 + 80
43 u = 430

1 u = 430 ÷ 43 = 10

Value of ten-cent coins
= 3 u x 10
= 3 x 10 x 10
= 300¢

Value of fifty-cent coins
= 8 u x 50
= 8 x 10 x 50
= 4000¢

Total value of coins
= 300 + 4000
= 4300¢

100¢ = $1

Sum of money in the coin box
= 4300¢
= $43

Answer(s): $43