A coin bank contains some ten-cent and fifty-cent coins in the ratio of 5 : 4.
When 11 fifty-cent coins are taken out and
exchanged with some ten-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) 10-cent |
(2) 50-cent |
Make p the same. (2) x 9 = (4) |
Before |
25 u |
5 u |
4 u |
36 u |
Change |
+ 275 |
+ 55 |
- 11 |
- 99 |
After |
45 p |
9 p |
5 p |
45 p |
Value of 11 fifty-cent coins
= 11 x 50
= 550¢
Number of ten-cent coins to exchange for
= 550 ÷ 10
= 55
5 u + 55 = 9 p --- (1)
4 u - 11 = 5 p --- (2)
Make p the same.
(1)
x 5 25 u + 275 = 45 p --- (3)
(2)
x 9 36 u - 99 = 45 p --- (4)
(4) = (3)
36 u - 99 = 25 u + 275
36 u - 25 u = 275 + 99
11 u = 374
1 u = 374 ÷ 11 = 34
Value of ten-cent coins
= 5 u x 10
= 5 x 34 x 10
= 1700¢
Value of fifty-cent coins
= 4 u x 50
= 4 x 34 x 50
= 6800¢
Total value of coins
= 1700 + 6800
= 8500¢
100¢ = $1
Sum of money in the coin box
= 8500¢
= $85
Answer(s): $85