A coin bank contains some twenty-cent and fifty-cent coins in the ratio of 5 : 6.
When 14 fifty-cent coins are taken out and
exchanged with some twenty-cent coins of the same value,
the ratio became 7 : 8.
Find the sum of money in the coin box in dollars.
|
Make p the same. (1) x 8 = (3) |
(1) 20-cent |
(2) 50-cent |
Make p the same. (2) x 7 = (4) |
Before |
40 u |
5 u |
6 u |
42 u |
Change |
+ 280 |
+ 35 |
- 14 |
- 98 |
After |
56 p |
7 p |
8 p |
56 p |
Value of 14 fifty-cent coins
= 14 x 50
= 700¢
Number of twenty-cent coins to exchange for
= 700 ÷ 20
= 35
5 u + 35 = 7 p --- (1)
6 u - 14 = 8 p --- (2)
Make p the same.
(1)
x 8 40 u + 280 = 56 p --- (3)
(2)
x 7 42 u - 98 = 56 p --- (4)
(4) = (3)
42 u - 98 = 40 u + 280
42 u - 40 u = 280 + 98
2 u = 378
1 u = 378 ÷ 2 = 189
Value of twenty-cent coins
= 5 u x 20
= 5 x 189 x 20
= 18900¢
Value of fifty-cent coins
= 6 u x 50
= 6 x 189 x 50
= 56700¢
Total value of coins
= 18900 + 56700
= 75600¢
100¢ = $1
Sum of money in the coin box
= 75600¢
= $756
Answer(s): $756