A coin bank contains some twenty-cent and fifty-cent coins in the ratio of 3 : 4. When 16 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 |
+ 320 |
+ 40 |
- 16 |
- 144 |
After |
72 p |
9 p |
8 p |
72 p |
Value of 50-cent coins taken out
= 16 x 0.50
= $8
Number of 20-cent coins put in
= 8 ÷ 0.20
= 40
(3) = (4)
36 u - 144 = 24 u + 320
36 u - 24 u = 320 + 144
16 u = 464
1 u = 464 ÷ 16 = 29
Number of 20-cent coins at first
= 3 u
= 3 x 29
= 87
Number of 50-cent coins at first
= 4 u
= 4 x 29
= 116
Sum of money in the coin box
= 87 x 0.20 + 116 x 0.50
= 17.40 + 58.00
= $75.40
Answer(s): $75.40