The number of fifty-cent coins in a basket was 200% more than the number of twenty-cent coins. 18 fifty-cent coins were taken out and exchanged for twenty-cent coins. The number of 50-cent coins became
37 less than the number of 20-cent coins. How much money is there in the basket?
|
Fifty-cent (1) |
Twenty-cent (2) |
Make u the same (2)x3 = (3) |
Before |
3 u |
1 u |
3 u |
Change |
- 18 |
+ 45 |
+ 135 |
After |
4 p |
7 p |
21 p |
100 + 200100=
300100 =
31 At first
Fifty-cent coins : Twenty-cent coins
3 : 1
1 -
37 =
47 In the end
Fifty-cent coins : Twenty-cent coins
4 : 7
Total value of 50-cent coins to be taken out
= 18 x 50
= 900¢
Total number of 20-cent coins to be exchanged for
= 900 ÷ 20
= 45
Notice that the number of 20-cent coins is 1 u at first. So, instead of making p the same, we can make u the same so we create one extra equation instead of 2.
3 u - 18 = 4 p
3 u = 4 p + 18 --- (1)
1 u + 45 = 7 p --- (2)
(2)x3
3 u + 135 = 21 p
3 u = 21 p - 135 --- (3)
(3) = (1)
21 p - 135 = 4 p + 18
21 p - 4 p = 18 + 135
17 p = 153
1 p = 153 ÷ 17 = 9
The total value of the coins at first and in the end remains unchanged.
Total value of fifty-cent coins in the end
= 4 p x 50
= 4 x 9 x 50
= 1800¢
Total value of twenty-cent coins in the end
= 7 p x 20
= 7 x 9 x 20
= 1260¢
Total value of the coins
= 1800 + 1260
= 3060¢
= $30.60
Answer(s): $30.60