A coin bank contains some five-cent and fifty-cent coins in the ratio of 5 : 6.
When 6 fifty-cent coins are taken out and
exchanged with some five-cent coins of the same value,
the ratio became 8 : 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 8 = (4) |
Before |
35 u |
5 u |
6 u |
48 u |
Change |
+ 420 |
+ 60 |
- 6 |
- 48 |
After |
56 p |
8 p |
7 p |
56 p |
Value of 6 fifty-cent coins
= 6 x 50
= 300¢
Number of five-cent coins to exchange for
= 300 ÷ 5
= 60
5 u + 60 = 8 p --- (1)
6 u - 6 = 7 p --- (2)
Make p the same.
(1)
x 7 35 u + 420 = 56 p --- (3)
(2)
x 8 48 u - 48 = 56 p --- (4)
(4) = (3)
48 u - 48 = 35 u + 420
48 u - 35 u = 420 + 48
13 u = 468
1 u = 468 ÷ 13 = 36
Value of five-cent coins
= 5 u x 5
= 5 x 36 x 5
= 900¢
Value of fifty-cent coins
= 6 u x 50
= 6 x 36 x 50
= 10800¢
Total value of coins
= 900 + 10800
= 11700¢
100¢ = $1
Sum of money in the coin box
= 11700¢
= $117
Answer(s): $117