A coin bank contains some twenty-cent and fifty-cent coins in the ratio of 4 : 5. When 16 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 |
+ 240 |
+ 40 |
- 16 |
- 112 |
After |
42 p |
7 p |
6 p |
42 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)
35 u - 112 = 24 u + 240
35 u - 24 u = 240 + 112
16 u = 352
1 u = 352 ÷ 16 = 22
Number of 20-cent coins at first
= 4 u
= 4 x 22
= 88
Number of 50-cent coins at first
= 5 u
= 5 x 22
= 110
Sum of money in the coin box
= 88 x 0.20 + 110 x 0.50
= 17.60 + 55.00
= $72.60
Answer(s): $72.60