A coin bank contains some ten-cent and twenty-cent coins in the ratio of 3 : 4.
When 15 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 |
+ 210 |
+ 30 |
- 15 |
- 120 |
After |
56 p |
8 p |
7 p |
56 p |
Value of 15 twenty-cent coins
= 15 x 20
= 300¢
Number of ten-cent coins to exchange for
= 300 ÷ 10
= 30
3 u + 30 = 8 p --- (1)
4 u - 15 = 7 p --- (2)
Make p the same.
(1)
x 7 21 u + 210 = 56 p --- (3)
(2)
x 8 32 u - 120 = 56 p --- (4)
(4) = (3)
32 u - 120 = 21 u + 210
32 u - 21 u = 210 + 120
11 u = 330
1 u = 330 ÷ 11 = 30
Value of ten-cent coins
= 3 u x 10
= 3 x 30 x 10
= 900¢
Value of twenty-cent coins
= 4 u x 20
= 4 x 30 x 20
= 2400¢
Total value of coins
= 900 + 2400
= 3300¢
100¢ = $1
Sum of money in the coin box
= 3300¢
= $33
Answer(s): $33