A coin bank contains some ten-cent and fifty-cent coins in the ratio of 3 : 4. When 16 fifty-cent coins were taken out and replaced by some ten-cent coins, the ratio became 9 : 8. The total value of the ten-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)x8 = (3) |
10-cent (1) |
50-cent (2) |
Make p the same (2)x9 = (4) |
Before |
24 u |
3 u |
4 u |
36 u |
Change |
+ 640 |
+ 80 |
- 16 |
- 144 |
After |
72 p |
9 p |
8 p |
72 p |
Value of 50-cent coins taken out
= 16 x 0.50
= $8
Number of 10-cent coins put in
= 8 ÷ 0.10
= 80
(3) = (4)
36 u - 144 = 24 u + 640
36 u - 24 u = 640 + 144
56 u = 784
1 u = 784 ÷ 56 = 14
Number of 10-cent coins at first
= 3 u
= 3 x 14
= 42
Number of 50-cent coins at first
= 4 u
= 4 x 14
= 56
Sum of money in the coin box
= 42 x 0.10 + 56 x 0.50
= 4.20 + 28.00
= $32.20
Answer(s): $32.20