A coin bank contains some twenty-cent and fifty-cent coins in the ratio of 3 : 4. When 12 fifty-cent coins were taken out and replaced by some twenty-cent coins, the ratio became 9 : 8. 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)x8 = (3) |
20-cent (1) |
50-cent (2) |
Make p the same (2)x9 = (4) |
Before |
24 u |
3 u |
4 u |
36 u |
Change |
+ 240 |
+ 30 |
- 12 |
- 108 |
After |
72 p |
9 p |
8 p |
72 p |
Value of 50-cent coins taken out
= 12 x 0.50
= $6
Number of 20-cent coins put in
= 6 ÷ 0.20
= 30
(3) = (4)
36 u - 108 = 24 u + 240
36 u - 24 u = 240 + 108
6 u = 348
1 u = 348 ÷ 6 = 58
Number of 20-cent coins at first
= 3 u
= 3 x 58
= 174
Number of 50-cent coins at first
= 4 u
= 4 x 58
= 232
Sum of money in the coin box
= 174 x 0.20 + 232 x 0.50
= 34.80 + 116.00
= $150.80
Answer(s): $150.80