A coin bank contains some twenty-cent and fifty-cent coins in the ratio of 5 : 7.
When 6 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 |
40 u |
5 u |
7 u |
49 u |
Change |
+ 120 |
+ 15 |
- 6 |
- 42 |
After |
56 p |
7 p |
8 p |
56 p |
Value of 6 fifty-cent coins
= 6 x 50
= 300¢
Number of twenty-cent coins to exchange for
= 300 ÷ 20
= 15
5 u + 15 = 7 p --- (1)
7 u - 6 = 8 p --- (2)
Make p the same.
(1)
x 8 40 u + 120 = 56 p --- (3)
(2)
x 7 49 u - 42 = 56 p --- (4)
(4) = (3)
49 u - 42 = 40 u + 120
49 u - 40 u = 120 + 42
9 u = 162
1 u = 162 ÷ 9 = 18
Value of twenty-cent coins
= 5 u x 20
= 5 x 18 x 20
= 1800¢
Value of fifty-cent coins
= 7 u x 50
= 7 x 18 x 50
= 6300¢
Total value of coins
= 1800 + 6300
= 8100¢
100¢ = $1
Sum of money in the coin box
= 8100¢
= $81
Answer(s): $81