A coin bank contains some twenty-cent and fifty-cent coins in the ratio of 4 : 5. When 14 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 |
+ 210 |
+ 35 |
- 14 |
- 98 |
After |
42 p |
7 p |
6 p |
42 p |
Value of 50-cent coins taken out
= 14 x 0.50
= $7
Number of 20-cent coins put in
= 7 ÷ 0.20
= 35
(3) = (4)
35 u - 98 = 24 u + 210
35 u - 24 u = 210 + 98
11 u = 308
1 u = 308 ÷ 11 = 28
Number of 20-cent coins at first
= 4 u
= 4 x 28
= 112
Number of 50-cent coins at first
= 5 u
= 5 x 28
= 140
Sum of money in the coin box
= 112 x 0.20 + 140 x 0.50
= 22.40 + 70.00
= $92.40
Answer(s): $92.40