A coin bank contains some five-cent and fifty-cent coins in the ratio of 5 : 6.
When 10 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 |
+ 700 |
+ 100 |
- 10 |
- 80 |
After |
56 p |
8 p |
7 p |
56 p |
Value of 10 fifty-cent coins
= 10 x 50
= 500¢
Number of five-cent coins to exchange for
= 500 ÷ 5
= 100
5 u + 100 = 8 p --- (1)
6 u - 10 = 7 p --- (2)
Make p the same.
(1)
x 7 35 u + 700 = 56 p --- (3)
(2)
x 8 48 u - 80 = 56 p --- (4)
(4) = (3)
48 u - 80 = 35 u + 700
48 u - 35 u = 700 + 80
13 u = 780
1 u = 780 ÷ 13 = 60
Value of five-cent coins
= 5 u x 5
= 5 x 60 x 5
= 1500¢
Value of fifty-cent coins
= 6 u x 50
= 6 x 60 x 50
= 18000¢
Total value of coins
= 1500 + 18000
= 19500¢
100¢ = $1
Sum of money in the coin box
= 19500¢
= $195
Answer(s): $195