A coin bank contains some five-cent and twenty-cent coins in the ratio of 4 : 5.
When 15 twenty-cent coins are taken out and
exchanged with some five-cent coins of the same value,
the ratio became 6 : 7.
Find the sum of money in the coin box in dollars.
|
Make p the same. (1) x 7 = (3) |
(1) 5-cent |
(2) 20-cent |
Make p the same. (2) x 6 = (4) |
Before |
28 u |
4 u |
5 u |
30 u |
Change |
+ 420 |
+ 60 |
- 15 |
- 90 |
After |
42 p |
6 p |
7 p |
42 p |
Value of 15 twenty-cent coins
= 15 x 20
= 300¢
Number of five-cent coins to exchange for
= 300 ÷ 5
= 60
4 u + 60 = 6 p --- (1)
5 u - 15 = 7 p --- (2)
Make p the same.
(1)
x 7 28 u + 420 = 42 p --- (3)
(2)
x 6 30 u - 90 = 42 p --- (4)
(4) = (3)
30 u - 90 = 28 u + 420
30 u - 28 u = 420 + 90
2 u = 510
1 u = 510 ÷ 2 = 255
Value of five-cent coins
= 4 u x 5
= 4 x 255 x 5
= 5100¢
Value of twenty-cent coins
= 5 u x 20
= 5 x 255 x 20
= 25500¢
Total value of coins
= 5100 + 25500
= 30600¢
100¢ = $1
Sum of money in the coin box
= 30600¢
= $306
Answer(s): $306