A coin bank contains some five-cent and fifty-cent coins in the ratio of 2 : 7.
When 20 fifty-cent coins are taken out and
exchanged with some five-cent coins of the same value,
the ratio became 6 : 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 6 = (4) |
Before |
10 u |
2 u |
7 u |
42 u |
Change |
+ 1000 |
+ 200 |
- 20 |
- 120 |
After |
30 p |
6 p |
5 p |
30 p |
Value of 20 fifty-cent coins
= 20 x 50
= 1000¢
Number of five-cent coins to exchange for
= 1000 ÷ 5
= 200
2 u + 200 = 6 p --- (1)
7 u - 20 = 5 p --- (2)
Make p the same.
(1)
x 5 10 u + 1000 = 30 p --- (3)
(2)
x 6 42 u - 120 = 30 p --- (4)
(4) = (3)
42 u - 120 = 10 u + 1000
42 u - 10 u = 1000 + 120
32 u = 1120
1 u = 1120 ÷ 32 = 35
Value of five-cent coins
= 2 u x 5
= 2 x 35 x 5
= 350¢
Value of fifty-cent coins
= 7 u x 50
= 7 x 35 x 50
= 12250¢
Total value of coins
= 350 + 12250
= 12600¢
100¢ = $1
Sum of money in the coin box
= 12600¢
= $126
Answer(s): $126