A coin bank contains some twenty-cent and fifty-cent coins in the ratio of 4 : 5. When 14 fifty-cent coins were taken out and replaced by some twenty-cent coins, the ratio became 8 : 7. The total value of the twenty-cent coins added was the same as the total value of the fifty-cent coins taken out. Find the sum of money in the coin box.
|
Make p the same (1)x7 = (3) |
20-cent (1) |
50-cent (2) |
Make p the same (2)x8 = (4) |
Before |
28 u |
4 u |
5 u |
40 u |
Change |
+ 245 |
+ 35 |
- 14 |
- 112 |
After |
56 p |
8 p |
7 p |
56 p |
Value of 50-cent coins taken out
= 14 x 0.50
= $7
Number of 20-cent coins put in
= 7 ÷ 0.20
= 35
(3) = (4)
40 u - 112 = 28 u + 245
40 u - 28 u = 245 + 112
7 u = 357
1 u = 357 ÷ 7 = 51
Number of 20-cent coins at first
= 4 u
= 4 x 51
= 204
Number of 50-cent coins at first
= 5 u
= 5 x 51
= 255
Sum of money in the coin box
= 204 x 0.20 + 255 x 0.50
= 40.80 + 127.50
= $168.30
Answer(s): $168.30