A coin bank contains some twenty-cent and fifty-cent coins in the ratio of 4 : 5. When 18 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 |
+ 315 |
+ 45 |
- 18 |
- 144 |
After |
56 p |
8 p |
7 p |
56 p |
Value of 50-cent coins taken out
= 18 x 0.50
= $9
Number of 20-cent coins put in
= 9 ÷ 0.20
= 45
(3) = (4)
40 u - 144 = 28 u + 315
40 u - 28 u = 315 + 144
17 u = 459
1 u = 459 ÷ 17 = 27
Number of 20-cent coins at first
= 4 u
= 4 x 27
= 108
Number of 50-cent coins at first
= 5 u
= 5 x 27
= 135
Sum of money in the coin box
= 108 x 0.20 + 135 x 0.50
= 21.60 + 67.50
= $89.10
Answer(s): $89.10