A coin bank contains some five-cent and fifty-cent coins in the ratio of 2 : 7.
When 7 fifty-cent coins are taken out and
exchanged with some five-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) 5-cent	(2) 50-cent	Make p the same. (2) x 10 = (4)
Before	14 u	2 u	7 u	70 u
Change	+ 490	+ 70	- 7	- 70
After	70 p	10 p	7 p	70 p

Value of 7 fifty-cent coins
= 7 x 50
= 350¢

Number of five-cent coins to exchange for
= 350 ÷ 5
= 70

2 u + 70 = 10 p --- (1)
7 u - 7 = 7 p --- (2)

Make p the same.

(1) _{x 7}
14 u + 490 = 70 p --- (3)

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

(4) = (3)
70 u - 70 = 14 u + 490
70 u - 14 u = 490 + 70
56 u = 560

1 u = 560 ÷ 56 = 10

Value of five-cent coins
= 2 u x 5
= 2 x 10 x 5
= 100¢

Value of fifty-cent coins
= 7 u x 50
= 7 x 10 x 50
= 3500¢

Total value of coins
= 100 + 3500
= 3600¢

100¢ = $1

Sum of money in the coin box
= 3600¢
= $36

Answer(s): $36