A coin bank contains some five-cent and twenty-cent coins in the ratio of 5 : 6.
When 20 twenty-cent coins are taken out and
exchanged with some five-cent coins of the same value,
the ratio became 9 : 5.
Find the sum of money in the coin box in dollars.
|
Make p the same. (1) x 5 = (3) |
(1) 5-cent |
(2) 20-cent |
Make p the same. (2) x 9 = (4) |
Before |
25 u |
5 u |
6 u |
54 u |
Change |
+ 400 |
+ 80 |
- 20 |
- 180 |
After |
45 p |
9 p |
5 p |
45 p |
Value of 20 twenty-cent coins
= 20 x 20
= 400¢
Number of five-cent coins to exchange for
= 400 ÷ 5
= 80
5 u + 80 = 9 p --- (1)
6 u - 20 = 5 p --- (2)
Make p the same.
(1)
x 5 25 u + 400 = 45 p --- (3)
(2)
x 9 54 u - 180 = 45 p --- (4)
(4) = (3)
54 u - 180 = 25 u + 400
54 u - 25 u = 400 + 180
29 u = 580
1 u = 580 ÷ 29 = 20
Value of five-cent coins
= 5 u x 5
= 5 x 20 x 5
= 500¢
Value of twenty-cent coins
= 6 u x 20
= 6 x 20 x 20
= 2400¢
Total value of coins
= 500 + 2400
= 2900¢
100¢ = $1
Sum of money in the coin box
= 2900¢
= $29
Answer(s): $29