A coin bank contains some ten-cent and fifty-cent coins in the ratio of 5 : 6. When 15 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 |
40 u |
5 u |
6 u |
54 u |
Change |
+ 600 |
+ 75 |
- 15 |
- 135 |
After |
72 p |
9 p |
8 p |
72 p |
Value of 50-cent coins taken out
= 15 x 0.50
= $7.5
Number of 10-cent coins put in
= 7.5 ÷ 0.10
= 75
(3) = (4)
54 u - 135 = 40 u + 600
54 u - 40 u = 600 + 135
35 u = 735
1 u = 735 ÷ 35 = 21
Number of 10-cent coins at first
= 5 u
= 5 x 21
= 105
Number of 50-cent coins at first
= 6 u
= 6 x 21
= 126
Sum of money in the coin box
= 105 x 0.10 + 126 x 0.50
= 10.50 + 63.00
= $73.50
Answer(s): $73.50