A coin bank contains some ten-cent and fifty-cent coins in the ratio of 5 : 8.
When 8 fifty-cent coins are taken out and
exchanged with some ten-cent coins of the same value,
the ratio became 10 : 7.
Find the sum of money in the coin box in dollars.
|
Make p the same. (1) x 7 = (3) |
(1) 10-cent |
(2) 50-cent |
Make p the same. (2) x 10 = (4) |
Before |
35 u |
5 u |
8 u |
80 u |
Change |
+ 280 |
+ 40 |
- 8 |
- 80 |
After |
70 p |
10 p |
7 p |
70 p |
Value of 8 fifty-cent coins
= 8 x 50
= 400¢
Number of ten-cent coins to exchange for
= 400 ÷ 10
= 40
5 u + 40 = 10 p --- (1)
8 u - 8 = 7 p --- (2)
Make p the same.
(1)
x 7 35 u + 280 = 70 p --- (3)
(2)
x 10 80 u - 80 = 70 p --- (4)
(4) = (3)
80 u - 80 = 35 u + 280
80 u - 35 u = 280 + 80
45 u = 360
1 u = 360 ÷ 45 = 8
Value of ten-cent coins
= 5 u x 10
= 5 x 8 x 10
= 400¢
Value of fifty-cent coins
= 8 u x 50
= 8 x 8 x 50
= 3200¢
Total value of coins
= 400 + 3200
= 3600¢
100¢ = $1
Sum of money in the coin box
= 3600¢
= $36
Answer(s): $36