A coin bank contains some ten-cent and fifty-cent coins in the ratio of 5 : 6.
When 8 fifty-cent coins are taken out and
exchanged with some ten-cent coins of the same value,
the ratio became 9 : 8.
Find the sum of money in the coin box in dollars.
|
Make p the same. (1) x 8 = (3) |
(1) 10-cent |
(2) 50-cent |
Make p the same. (2) x 9 = (4) |
Before |
40 u |
5 u |
6 u |
54 u |
Change |
+ 320 |
+ 40 |
- 8 |
- 72 |
After |
72 p |
9 p |
8 p |
72 p |
Value of 8 fifty-cent coins
= 8 x 50
= 400¢
Number of ten-cent coins to exchange for
= 400 ÷ 10
= 40
5 u + 40 = 9 p --- (1)
6 u - 8 = 8 p --- (2)
Make p the same.
(1)
x 8 40 u + 320 = 72 p --- (3)
(2)
x 9 54 u - 72 = 72 p --- (4)
(4) = (3)
54 u - 72 = 40 u + 320
54 u - 40 u = 320 + 72
14 u = 392
1 u = 392 ÷ 14 = 28
Value of ten-cent coins
= 5 u x 10
= 5 x 28 x 10
= 1400¢
Value of fifty-cent coins
= 6 u x 50
= 6 x 28 x 50
= 8400¢
Total value of coins
= 1400 + 8400
= 9800¢
100¢ = $1
Sum of money in the coin box
= 9800¢
= $98
Answer(s): $98