The number of fifty-cent coins in a bag was 100% more than the number of ten-cent coins. 9 fifty-cent coins were taken out and exchanged for ten-cent coins. The number of 50-cent coins became
47 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 |
- 9 |
+ 45 |
+ 90 |
After |
3 p |
7 p |
14 p |
100 + 100100=
200100 =
21 At first
Fifty-cent coins : Ten-cent coins
2 : 1
1 -
47 =
37 In the end
Fifty-cent coins : Ten-cent coins
3 : 7
Total value of 50-cent coins to be taken out
= 9 x 50
= 450¢
Total number of 10-cent coins to be exchanged for
= 450 ÷ 10
= 45
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 - 9 = 3 p
2 u = 3 p + 9 --- (1)
1 u + 45 = 7 p --- (2)
(2)x2
2 u + 90 = 14 p
2 u = 14 p - 90 --- (3)
(3) = (1)
14 p - 90 = 3 p + 9
14 p - 3 p = 9 + 90
11 p = 99
1 p = 99 ÷ 11 = 9
The total value of the coins at first and in the end remains unchanged.
Total value of fifty-cent coins in the end
= 3 p x 50
= 3 x 9 x 50
= 1350¢
Total value of ten-cent coins in the end
= 7 p x 10
= 7 x 9 x 10
= 630¢
Total value of the coins
= 1350 + 630
= 1980¢
= $19.80
Answer(s): $19.80