A coin bank contains some twenty-cent and fifty-cent coins in the ratio of 4 : 5. When 12 fifty-cent coins were taken out and replaced by some twenty-cent coins, the ratio became 7 : 6. 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)x6 = (3) |
20-cent (1) |
50-cent (2) |
Make p the same (2)x7 = (4) |
Before |
24 u |
4 u |
5 u |
35 u |
Change |
+ 180 |
+ 30 |
- 12 |
- 84 |
After |
42 p |
7 p |
6 p |
42 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)
35 u - 84 = 24 u + 180
35 u - 24 u = 180 + 84
6 u = 264
1 u = 264 ÷ 6 = 44
Number of 20-cent coins at first
= 4 u
= 4 x 44
= 176
Number of 50-cent coins at first
= 5 u
= 5 x 44
= 220
Sum of money in the coin box
= 176 x 0.20 + 220 x 0.50
= 35.20 + 110.00
= $145.20
Answer(s): $145.20