A coin bank contains some ten-cent and fifty-cent coins in the ratio of 5 : 7.
When 18 fifty-cent coins are taken out and
exchanged with some ten-cent coins of the same value,
the ratio became 7 : 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 7 = (4) |
Before |
25 u |
5 u |
7 u |
49 u |
Change |
+ 450 |
+ 90 |
- 18 |
- 126 |
After |
35 p |
7 p |
5 p |
35 p |
Value of 18 fifty-cent coins
= 18 x 50
= 900¢
Number of ten-cent coins to exchange for
= 900 ÷ 10
= 90
5 u + 90 = 7 p --- (1)
7 u - 18 = 5 p --- (2)
Make p the same.
(1)
x 5 25 u + 450 = 35 p --- (3)
(2)
x 7 49 u - 126 = 35 p --- (4)
(4) = (3)
49 u - 126 = 25 u + 450
49 u - 25 u = 450 + 126
24 u = 576
1 u = 576 ÷ 24 = 24
Value of ten-cent coins
= 5 u x 10
= 5 x 24 x 10
= 1200¢
Value of fifty-cent coins
= 7 u x 50
= 7 x 24 x 50
= 8400¢
Total value of coins
= 1200 + 8400
= 9600¢
100¢ = $1
Sum of money in the coin box
= 9600¢
= $96
Answer(s): $96