A coin bank contains some five-cent and fifty-cent coins in the ratio of 5 : 4.
When 16 fifty-cent coins are taken out and
exchanged with some five-cent coins of the same value,
the ratio became 7 : 5.
Find the sum of money in the coin box in dollars.
|
Make p the same. (1) x 5 = (3) |
(1) 5-cent |
(2) 50-cent |
Make p the same. (2) x 7 = (4) |
Before |
25 u |
5 u |
4 u |
28 u |
Change |
+ 800 |
+ 160 |
- 16 |
- 112 |
After |
35 p |
7 p |
5 p |
35 p |
Value of 16 fifty-cent coins
= 16 x 50
= 800¢
Number of five-cent coins to exchange for
= 800 ÷ 5
= 160
5 u + 160 = 7 p --- (1)
4 u - 16 = 5 p --- (2)
Make p the same.
(1)
x 5 25 u + 800 = 35 p --- (3)
(2)
x 7 28 u - 112 = 35 p --- (4)
(4) = (3)
28 u - 112 = 25 u + 800
28 u - 25 u = 800 + 112
3 u = 912
1 u = 912 ÷ 3 = 304
Value of five-cent coins
= 5 u x 5
= 5 x 304 x 5
= 7600¢
Value of fifty-cent coins
= 4 u x 50
= 4 x 304 x 50
= 60800¢
Total value of coins
= 7600 + 60800
= 68400¢
100¢ = $1
Sum of money in the coin box
= 68400¢
= $684
Answer(s): $684