A coin bank contains some five-cent and fifty-cent coins in the ratio of 5 : 4.
When 12 fifty-cent coins are taken out and
exchanged with some five-cent coins of the same value,
the ratio became 10 : 7.
Find the sum of money in the coin box in dollars.
|
Make p the same. (1) x 7 = (3) |
(1) 5-cent |
(2) 50-cent |
Make p the same. (2) x 10 = (4) |
Before |
35 u |
5 u |
4 u |
40 u |
Change |
+ 840 |
+ 120 |
- 12 |
- 120 |
After |
70 p |
10 p |
7 p |
70 p |
Value of 12 fifty-cent coins
= 12 x 50
= 600¢
Number of five-cent coins to exchange for
= 600 ÷ 5
= 120
5 u + 120 = 10 p --- (1)
4 u - 12 = 7 p --- (2)
Make p the same.
(1)
x 7 35 u + 840 = 70 p --- (3)
(2)
x 10 40 u - 120 = 70 p --- (4)
(4) = (3)
40 u - 120 = 35 u + 840
40 u - 35 u = 840 + 120
5 u = 960
1 u = 960 ÷ 5 = 192
Value of five-cent coins
= 5 u x 5
= 5 x 192 x 5
= 4800¢
Value of fifty-cent coins
= 4 u x 50
= 4 x 192 x 50
= 38400¢
Total value of coins
= 4800 + 38400
= 43200¢
100¢ = $1
Sum of money in the coin box
= 43200¢
= $432
Answer(s): $432