A coin bank contains some twenty-cent and fifty-cent coins in the ratio of 2 : 7.
When 20 fifty-cent coins are taken out and
exchanged with some twenty-cent coins of the same value,
the ratio became 7 : 5.
Find the sum of money in the coin box in dollars.
|
Make p the same. (1) x 5 = (3) |
(1) 20-cent |
(2) 50-cent |
Make p the same. (2) x 7 = (4) |
Before |
10 u |
2 u |
7 u |
49 u |
Change |
+ 250 |
+ 50 |
- 20 |
- 140 |
After |
35 p |
7 p |
5 p |
35 p |
Value of 20 fifty-cent coins
= 20 x 50
= 1000¢
Number of twenty-cent coins to exchange for
= 1000 ÷ 20
= 50
2 u + 50 = 7 p --- (1)
7 u - 20 = 5 p --- (2)
Make p the same.
(1)
x 5 10 u + 250 = 35 p --- (3)
(2)
x 7 49 u - 140 = 35 p --- (4)
(4) = (3)
49 u - 140 = 10 u + 250
49 u - 10 u = 250 + 140
39 u = 390
1 u = 390 ÷ 39 = 10
Value of twenty-cent coins
= 2 u x 20
= 2 x 10 x 20
= 400¢
Value of fifty-cent coins
= 7 u x 50
= 7 x 10 x 50
= 3500¢
Total value of coins
= 400 + 3500
= 3900¢
100¢ = $1
Sum of money in the coin box
= 3900¢
= $39
Answer(s): $39