A coin bank contains some ten-cent and twenty-cent coins in the ratio of 3 : 4.
When 6 twenty-cent coins are taken out and
exchanged with some ten-cent coins of the same value,
the ratio became 6 : 7.
Find the sum of money in the coin box in dollars.
|
Make p the same. (1) x 7 = (3) |
(1) 10-cent |
(2) 20-cent |
Make p the same. (2) x 6 = (4) |
Before |
21 u |
3 u |
4 u |
24 u |
Change |
+ 84 |
+ 12 |
- 6 |
- 36 |
After |
42 p |
6 p |
7 p |
42 p |
Value of 6 twenty-cent coins
= 6 x 20
= 120¢
Number of ten-cent coins to exchange for
= 120 ÷ 10
= 12
3 u + 12 = 6 p --- (1)
4 u - 6 = 7 p --- (2)
Make p the same.
(1)
x 7 21 u + 84 = 42 p --- (3)
(2)
x 6 24 u - 36 = 42 p --- (4)
(4) = (3)
24 u - 36 = 21 u + 84
24 u - 21 u = 84 + 36
3 u = 120
1 u = 120 ÷ 3 = 40
Value of ten-cent coins
= 3 u x 10
= 3 x 40 x 10
= 1200¢
Value of twenty-cent coins
= 4 u x 20
= 4 x 40 x 20
= 3200¢
Total value of coins
= 1200 + 3200
= 4400¢
100¢ = $1
Sum of money in the coin box
= 4400¢
= $44
Answer(s): $44