A coin bank contains some twenty-cent and fifty-cent coins in the ratio of 4 : 5.
When 15 fifty-cent coins are taken out and
exchanged with some twenty-cent coins of the same value,
the ratio became 7 : 6.
Find the sum of money in the coin box in dollars.
|
Make p the same. (1) x 6 = (3) |
(1) 20-cent |
(2) 50-cent |
Make p the same. (2) x 7 = (4) |
Before |
24 u |
4 u |
5 u |
35 u |
Change |
+ 225 |
+ 37.5 |
- 15 |
- 105 |
After |
42 p |
7 p |
6 p |
42 p |
Value of 15 fifty-cent coins
= 15 x 50
= 750¢
Number of twenty-cent coins to exchange for
= 750 ÷ 20
= 37.5
4 u + 37.5 = 7 p --- (1)
5 u - 15 = 6 p --- (2)
Make p the same.
(1)
x 6 24 u + 225 = 42 p --- (3)
(2)
x 7 35 u - 105 = 42 p --- (4)
(4) = (3)
35 u - 105 = 24 u + 225
35 u - 24 u = 225 + 105
11 u = 330
1 u = 330 ÷ 11 = 30
Value of twenty-cent coins
= 4 u x 20
= 4 x 30 x 20
= 2400¢
Value of fifty-cent coins
= 5 u x 50
= 5 x 30 x 50
= 7500¢
Total value of coins
= 2400 + 7500
= 9900¢
100¢ = $1
Sum of money in the coin box
= 9900¢
= $99
Answer(s): $99