A coin bank contains some ten-cent and fifty-cent coins in the ratio of 5 : 7.
When 6 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 |
+ 150 |
+ 30 |
- 6 |
- 42 |
After |
35 p |
7 p |
5 p |
35 p |
Value of 6 fifty-cent coins
= 6 x 50
= 300¢
Number of ten-cent coins to exchange for
= 300 ÷ 10
= 30
5 u + 30 = 7 p --- (1)
7 u - 6 = 5 p --- (2)
Make p the same.
(1)
x 5 25 u + 150 = 35 p --- (3)
(2)
x 7 49 u - 42 = 35 p --- (4)
(4) = (3)
49 u - 42 = 25 u + 150
49 u - 25 u = 150 + 42
24 u = 192
1 u = 192 ÷ 24 = 8
Value of ten-cent coins
= 5 u x 10
= 5 x 8 x 10
= 400¢
Value of fifty-cent coins
= 7 u x 50
= 7 x 8 x 50
= 2800¢
Total value of coins
= 400 + 2800
= 3200¢
100¢ = $1
Sum of money in the coin box
= 3200¢
= $32
Answer(s): $32