The number of fifty-cent coins in a bag was 100% more than the number of ten-cent coins. 5 fifty-cent coins were taken out and exchanged for ten-cent coins. The number of 50-cent coins became
38 less than the number of 10-cent coins. How much money is there in the bag?
|
Fifty-cent (1) |
Ten-cent (2) |
Make u the same (2)x2 = (3) |
Before |
2 u |
1 u |
2 u |
Change |
- 5 |
+ 25 |
+ 50 |
After |
5 p |
8 p |
16 p |
100 + 100100=
200100 =
21 At first
Fifty-cent coins : Ten-cent coins
2 : 1
1 -
38 =
58 In the end
Fifty-cent coins : Ten-cent coins
5 : 8
Total value of 50-cent coins to be taken out
= 5 x 50
= 250¢
Total number of 10-cent coins to be exchanged for
= 250 ÷ 10
= 25
Notice that the number of 10-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 - 5 = 5 p
2 u = 5 p + 5 --- (1)
1 u + 25 = 8 p --- (2)
(2)x2
2 u + 50 = 16 p
2 u = 16 p - 50 --- (3)
(3) = (1)
16 p - 50 = 5 p + 5
16 p - 5 p = 5 + 50
11 p = 55
1 p = 55 ÷ 11 = 5
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 5 x 50
= 1250¢
Total value of ten-cent coins in the end
= 8 p x 10
= 8 x 5 x 10
= 400¢
Total value of the coins
= 1250 + 400
= 1650¢
= $16.50
Answer(s): $16.50