A coin bank contains some five-cent and fifty-cent coins in the ratio of 4 : 5.
When 20 fifty-cent coins are taken out and
exchanged with some five-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) 5-cent |
(2) 50-cent |
Make p the same. (2) x 7 = (4) |
Before |
32 u |
4 u |
5 u |
35 u |
Change |
+ 1600 |
+ 200 |
- 20 |
- 140 |
After |
56 p |
7 p |
8 p |
56 p |
Value of 20 fifty-cent coins
= 20 x 50
= 1000¢
Number of five-cent coins to exchange for
= 1000 ÷ 5
= 200
4 u + 200 = 7 p --- (1)
5 u - 20 = 8 p --- (2)
Make p the same.
(1)
x 8 32 u + 1600 = 56 p --- (3)
(2)
x 7 35 u - 140 = 56 p --- (4)
(4) = (3)
35 u - 140 = 32 u + 1600
35 u - 32 u = 1600 + 140
3 u = 1740
1 u = 1740 ÷ 3 = 580
Value of five-cent coins
= 4 u x 5
= 4 x 580 x 5
= 11600¢
Value of fifty-cent coins
= 5 u x 50
= 5 x 580 x 50
= 145000¢
Total value of coins
= 11600 + 145000
= 156600¢
100¢ = $1
Sum of money in the coin box
= 156600¢
= $1566
Answer(s): $1566