A coin bank contains some ten-cent and twenty-cent coins in the ratio of 3 : 4.
When 10 twenty-cent coins are taken out and
exchanged with some ten-cent coins of the same value,
the ratio became 8 : 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 8 = (4) |
Before |
21 u |
3 u |
4 u |
32 u |
Change |
+ 140 |
+ 20 |
- 10 |
- 80 |
After |
56 p |
8 p |
7 p |
56 p |
Value of 10 twenty-cent coins
= 10 x 20
= 200¢
Number of ten-cent coins to exchange for
= 200 ÷ 10
= 20
3 u + 20 = 8 p --- (1)
4 u - 10 = 7 p --- (2)
Make p the same.
(1)
x 7 21 u + 140 = 56 p --- (3)
(2)
x 8 32 u - 80 = 56 p --- (4)
(4) = (3)
32 u - 80 = 21 u + 140
32 u - 21 u = 140 + 80
11 u = 220
1 u = 220 ÷ 11 = 20
Value of ten-cent coins
= 3 u x 10
= 3 x 20 x 10
= 600¢
Value of twenty-cent coins
= 4 u x 20
= 4 x 20 x 20
= 1600¢
Total value of coins
= 600 + 1600
= 2200¢
100¢ = $1
Sum of money in the coin box
= 2200¢
= $22
Answer(s): $22