A coin bank contains some twenty-cent and fifty-cent coins in the ratio of 4 : 5.
When 5 fifty-cent coins are taken out and
exchanged with some twenty-cent coins of the same value,
the ratio became 7 : 6.
Find the sum of money in the coin box in dollars.
|
Make p the same. (1) x 6 = (3) |
(1) 20-cent |
(2) 50-cent |
Make p the same. (2) x 7 = (4) |
Before |
24 u |
4 u |
5 u |
35 u |
Change |
+ 75 |
+ 12.5 |
- 5 |
- 35 |
After |
42 p |
7 p |
6 p |
42 p |
Value of 5 fifty-cent coins
= 5 x 50
= 250¢
Number of twenty-cent coins to exchange for
= 250 ÷ 20
= 12.5
4 u + 12.5 = 7 p --- (1)
5 u - 5 = 6 p --- (2)
Make p the same.
(1)
x 6 24 u + 75 = 42 p --- (3)
(2)
x 7 35 u - 35 = 42 p --- (4)
(4) = (3)
35 u - 35 = 24 u + 75
35 u - 24 u = 75 + 35
11 u = 110
1 u = 110 ÷ 11 = 10
Value of twenty-cent coins
= 4 u x 20
= 4 x 10 x 20
= 800¢
Value of fifty-cent coins
= 5 u x 50
= 5 x 10 x 50
= 2500¢
Total value of coins
= 800 + 2500
= 3300¢
100¢ = $1
Sum of money in the coin box
= 3300¢
= $33
Answer(s): $33