A coin bank contains some five-cent and fifty-cent coins in the ratio of 2 : 5.
When 18 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 |
14 u |
2 u |
5 u |
50 u |
Change |
+ 1260 |
+ 180 |
- 18 |
- 180 |
After |
70 p |
10 p |
7 p |
70 p |
Value of 18 fifty-cent coins
= 18 x 50
= 900¢
Number of five-cent coins to exchange for
= 900 ÷ 5
= 180
2 u + 180 = 10 p --- (1)
5 u - 18 = 7 p --- (2)
Make p the same.
(1)
x 7 14 u + 1260 = 70 p --- (3)
(2)
x 10 50 u - 180 = 70 p --- (4)
(4) = (3)
50 u - 180 = 14 u + 1260
50 u - 14 u = 1260 + 180
36 u = 1440
1 u = 1440 ÷ 36 = 40
Value of five-cent coins
= 2 u x 5
= 2 x 40 x 5
= 400¢
Value of fifty-cent coins
= 5 u x 50
= 5 x 40 x 50
= 10000¢
Total value of coins
= 400 + 10000
= 10400¢
100¢ = $1
Sum of money in the coin box
= 10400¢
= $104
Answer(s): $104