A coin bank contains some twenty-cent and fifty-cent coins in the ratio of 4 : 5.
When 10 fifty-cent coins are taken out and
exchanged with some twenty-cent coins of the same value,
the ratio became 7 : 8.
Find the sum of money in the coin box in dollars.
|
Make p the same. (1) x 8 = (3) |
(1) 20-cent |
(2) 50-cent |
Make p the same. (2) x 7 = (4) |
Before |
32 u |
4 u |
5 u |
35 u |
Change |
+ 200 |
+ 25 |
- 10 |
- 70 |
After |
56 p |
7 p |
8 p |
56 p |
Value of 10 fifty-cent coins
= 10 x 50
= 500¢
Number of twenty-cent coins to exchange for
= 500 ÷ 20
= 25
4 u + 25 = 7 p --- (1)
5 u - 10 = 8 p --- (2)
Make p the same.
(1)
x 8 32 u + 200 = 56 p --- (3)
(2)
x 7 35 u - 70 = 56 p --- (4)
(4) = (3)
35 u - 70 = 32 u + 200
35 u - 32 u = 200 + 70
3 u = 270
1 u = 270 ÷ 3 = 90
Value of twenty-cent coins
= 4 u x 20
= 4 x 90 x 20
= 7200¢
Value of fifty-cent coins
= 5 u x 50
= 5 x 90 x 50
= 22500¢
Total value of coins
= 7200 + 22500
= 29700¢
100¢ = $1
Sum of money in the coin box
= 29700¢
= $297
Answer(s): $297