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 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 |
21 u |
3 u |
4 u |
32 u |
Change |
+ 210 |
+ 30 |
- 12 |
- 96 |
After |
56 p |
8 p |
7 p |
56 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)
32 u - 96 = 21 u + 210
32 u - 21 u = 210 + 96
9 u = 306
1 u = 306 ÷ 9 = 34
Number of 20-cent coins at first
= 3 u
= 3 x 34
= 102
Number of 50-cent coins at first
= 4 u
= 4 x 34
= 136
Sum of money in the coin box
= 102 x 0.20 + 136 x 0.50
= 20.40 + 68.00
= $88.40
Answer(s): $88.40