The number of fifty-cent coins in a basket was 100% more than the number of twenty-cent coins. 6 fifty-cent coins were taken out and exchanged for twenty-cent coins. The number of 50-cent coins became
27 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)x2 = (3) |
Before |
2 u |
1 u |
2 u |
Change |
- 6 |
+ 15 |
+ 30 |
After |
5 p |
7 p |
14 p |
100 + 100100=
200100 =
21 At first
Fifty-cent coins : Twenty-cent coins
2 : 1
1 -
27 =
57 In the end
Fifty-cent coins : Twenty-cent coins
5 : 7
Total value of 50-cent coins to be taken out
= 6 x 50
= 300¢
Total number of 20-cent coins to be exchanged for
= 300 ÷ 20
= 15
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.
2 u - 6 = 5 p
2 u = 5 p + 6 --- (1)
1 u + 15 = 7 p --- (2)
(2)x2
2 u + 30 = 14 p
2 u = 14 p - 30 --- (3)
(3) = (1)
14 p - 30 = 5 p + 6
14 p - 5 p = 6 + 30
9 p = 36
1 p = 36 ÷ 9 = 4
The total value of the coins at first and in the end remains unchanged.
Total value of fifty-cent coins in the end
= 5 p x 50
= 5 x 4 x 50
= 1000¢
Total value of twenty-cent coins in the end
= 7 p x 20
= 7 x 4 x 20
= 560¢
Total value of the coins
= 1000 + 560
= 1560¢
= $15.60
Answer(s): $15.60