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 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 |
18 u |
3 u |
4 u |
28 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)
28 u - 84 = 18 u + 180
28 u - 18 u = 180 + 84
12 u = 264
1 u = 264 ÷ 12 = 22
Number of 20-cent coins at first
= 3 u
= 3 x 22
= 66
Number of 50-cent coins at first
= 4 u
= 4 x 22
= 88
Sum of money in the coin box
= 66 x 0.20 + 88 x 0.50
= 13.20 + 44.00
= $57.20
Answer(s): $57.20