A coin bank contains some ten-cent and fifty-cent coins in the ratio of 4 : 5. When 27 fifty-cent coins were taken out and replaced by some ten-cent coins, the ratio became 7 : 6. 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)x6 = (3) |
10-cent (1) |
50-cent (2) |
Make p the same (2)x7 = (4) |
Before |
24 u |
4 u |
5 u |
35 u |
Change |
+ 810 |
+ 135 |
- 27 |
- 189 |
After |
42 p |
7 p |
6 p |
42 p |
Value of 50-cent coins taken out
= 27 x 0.50
= $13.5
Number of 10-cent coins put in
= 13.5 ÷ 0.10
= 135
(3) = (4)
35 u - 189 = 24 u + 810
35 u - 24 u = 810 + 189
111 u = 999
1 u = 999 ÷ 111 = 9
Number of 10-cent coins at first
= 4 u
= 4 x 9
= 36
Number of 50-cent coins at first
= 5 u
= 5 x 9
= 45
Sum of money in the coin box
= 36 x 0.10 + 45 x 0.50
= 3.60 + 22.50
= $26.10
Answer(s): $26.10