A coin bank contains some twenty-cent and fifty-cent coins in the ratio of 5 : 4.
When 14 fifty-cent coins are taken out and
exchanged with some twenty-cent coins of the same value,
the ratio became 10 : 7.
Find the sum of money in the coin box in dollars.
|
Make p the same. (1) x 7 = (3) |
(1) 20-cent |
(2) 50-cent |
Make p the same. (2) x 10 = (4) |
Before |
35 u |
5 u |
4 u |
40 u |
Change |
+ 245 |
+ 35 |
- 14 |
- 140 |
After |
70 p |
10 p |
7 p |
70 p |
Value of 14 fifty-cent coins
= 14 x 50
= 700¢
Number of twenty-cent coins to exchange for
= 700 ÷ 20
= 35
5 u + 35 = 10 p --- (1)
4 u - 14 = 7 p --- (2)
Make p the same.
(1)
x 7 35 u + 245 = 70 p --- (3)
(2)
x 10 40 u - 140 = 70 p --- (4)
(4) = (3)
40 u - 140 = 35 u + 245
40 u - 35 u = 245 + 140
5 u = 385
1 u = 385 ÷ 5 = 77
Value of twenty-cent coins
= 5 u x 20
= 5 x 77 x 20
= 7700¢
Value of fifty-cent coins
= 4 u x 50
= 4 x 77 x 50
= 15400¢
Total value of coins
= 7700 + 15400
= 23100¢
100¢ = $1
Sum of money in the coin box
= 23100¢
= $231
Answer(s): $231