The number of fifty-cent coins in a bag was 300% more than the number of twenty-cent coins. 20 fifty-cent coins were taken out and exchanged for twenty-cent coins. The number of 50-cent coins became
716 less than the number of 20-cent coins. How much money is there in the bag?
|
Fifty-cent (1) |
Twenty-cent (2) |
Make u the same (2)x4 = (3) |
Before |
4 u |
1 u |
4 u |
Change |
- 20 |
+ 50 |
+ 200 |
After |
9 p |
16 p |
64 p |
100 + 300100=
400100 =
41 At first
Fifty-cent coins : Twenty-cent coins
4 : 1
1 -
716 =
916 In the end
Fifty-cent coins : Twenty-cent coins
9 : 16
Total value of 50-cent coins to be taken out
= 20 x 50
= 1000¢
Total number of 20-cent coins to be exchanged for
= 1000 ÷ 20
= 50
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.
4 u - 20 = 9 p
4 u = 9 p + 20 --- (1)
1 u + 50 = 16 p --- (2)
(2)x4
4 u + 200 = 64 p
4 u = 64 p - 200 --- (3)
(3) = (1)
64 p - 200 = 9 p + 20
64 p - 9 p = 20 + 200
55 p = 220
1 p = 220 ÷ 55 = 4
The total value of the coins at first and in the end remains unchanged.
Total value of fifty-cent coins in the end
= 9 p x 50
= 9 x 4 x 50
= 1800¢
Total value of twenty-cent coins in the end
= 16 p x 20
= 16 x 4 x 20
= 1280¢
Total value of the coins
= 1800 + 1280
= 3080¢
= $30.80
Answer(s): $30.80