A coin bank contains some ten-cent and fifty-cent coins in the ratio of 4 : 5. When 26 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 |
32 u |
4 u |
5 u |
45 u |
Change |
+ 1040 |
+ 130 |
- 26 |
- 234 |
After |
72 p |
9 p |
8 p |
72 p |
Value of 50-cent coins taken out
= 26 x 0.50
= $13
Number of 10-cent coins put in
= 13 ÷ 0.10
= 130
(3) = (4)
45 u - 234 = 32 u + 1040
45 u - 32 u = 1040 + 234
98 u = 1274
1 u = 1274 ÷ 98 = 13
Number of 10-cent coins at first
= 4 u
= 4 x 13
= 52
Number of 50-cent coins at first
= 5 u
= 5 x 13
= 65
Sum of money in the coin box
= 52 x 0.10 + 65 x 0.50
= 5.20 + 32.50
= $37.70
Answer(s): $37.70