A coin bank contains some five-cent and fifty-cent coins in the ratio of 5 : 6.
When 15 fifty-cent coins are taken out and
exchanged with some five-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) 5-cent |
(2) 50-cent |
Make p the same. (2) x 10 = (4) |
Before |
35 u |
5 u |
6 u |
60 u |
Change |
+ 1050 |
+ 150 |
- 15 |
- 150 |
After |
70 p |
10 p |
7 p |
70 p |
Value of 15 fifty-cent coins
= 15 x 50
= 750¢
Number of five-cent coins to exchange for
= 750 ÷ 5
= 150
5 u + 150 = 10 p --- (1)
6 u - 15 = 7 p --- (2)
Make p the same.
(1)
x 7 35 u + 1050 = 70 p --- (3)
(2)
x 10 60 u - 150 = 70 p --- (4)
(4) = (3)
60 u - 150 = 35 u + 1050
60 u - 35 u = 1050 + 150
25 u = 1200
1 u = 1200 ÷ 25 = 48
Value of five-cent coins
= 5 u x 5
= 5 x 48 x 5
= 1200¢
Value of fifty-cent coins
= 6 u x 50
= 6 x 48 x 50
= 14400¢
Total value of coins
= 1200 + 14400
= 15600¢
100¢ = $1
Sum of money in the coin box
= 15600¢
= $156
Answer(s): $156