A coin bank contains some twenty-cent and fifty-cent coins in the ratio of 5 : 6.
When 18 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 |
30 u |
5 u |
6 u |
42 u |
Change |
+ 270 |
+ 45 |
- 18 |
- 126 |
After |
42 p |
7 p |
6 p |
42 p |
Value of 18 fifty-cent coins
= 18 x 50
= 900¢
Number of twenty-cent coins to exchange for
= 900 ÷ 20
= 45
5 u + 45 = 7 p --- (1)
6 u - 18 = 6 p --- (2)
Make p the same.
(1)
x 6 30 u + 270 = 42 p --- (3)
(2)
x 7 42 u - 126 = 42 p --- (4)
(4) = (3)
42 u - 126 = 30 u + 270
42 u - 30 u = 270 + 126
12 u = 396
1 u = 396 ÷ 12 = 33
Value of twenty-cent coins
= 5 u x 20
= 5 x 33 x 20
= 3300¢
Value of fifty-cent coins
= 6 u x 50
= 6 x 33 x 50
= 9900¢
Total value of coins
= 3300 + 9900
= 13200¢
100¢ = $1
Sum of money in the coin box
= 13200¢
= $132
Answer(s): $132