A coin bank contains some five-cent and fifty-cent coins in the ratio of 2 : 5.
When 20 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 |
14 u |
2 u |
5 u |
40 u |
Change |
+ 1400 |
+ 200 |
- 20 |
- 160 |
After |
56 p |
8 p |
7 p |
56 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 = 8 p --- (1)
5 u - 20 = 7 p --- (2)
Make p the same.
(1)
x 7 14 u + 1400 = 56 p --- (3)
(2)
x 8 40 u - 160 = 56 p --- (4)
(4) = (3)
40 u - 160 = 14 u + 1400
40 u - 14 u = 1400 + 160
26 u = 1560
1 u = 1560 ÷ 26 = 60
Value of five-cent coins
= 2 u x 5
= 2 x 60 x 5
= 600¢
Value of fifty-cent coins
= 5 u x 50
= 5 x 60 x 50
= 15000¢
Total value of coins
= 600 + 15000
= 15600¢
100¢ = $1
Sum of money in the coin box
= 15600¢
= $156
Answer(s): $156