The number of twenty-cent coins in a bag was 200% more than the number of ten-cent coins. 17 twenty-cent coins were taken out and exchanged for ten-cent coins. The number of 20-cent coins became
37 less than the number of 10-cent coins. How much money is there in the bag?
|
Twenty-cent (1) |
Ten-cent (2) |
Make u the same (2)x3 = (3) |
Before |
3 u |
1 u |
3 u |
Change |
- 17 |
+ 34 |
+ 102 |
After |
4 p |
7 p |
21 p |
100 + 200100=
300100 =
31 At first
Twenty-cent coins : Ten-cent coins
3 : 1
1 -
37 =
47 In the end
Twenty-cent coins : Ten-cent coins
4 : 7
Total value of 20-cent coins to be taken out
= 17 x 20
= 340¢
Total number of 10-cent coins to be exchanged for
= 340 ÷ 10
= 34
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.
3 u - 17 = 4 p
3 u = 4 p + 17 --- (1)
1 u + 34 = 7 p --- (2)
(2)x3
3 u + 102 = 21 p
3 u = 21 p - 102 --- (3)
(3) = (1)
21 p - 102 = 4 p + 17
21 p - 4 p = 17 + 102
17 p = 119
1 p = 119 ÷ 17 = 7
The total value of the coins at first and in the end remains unchanged.
Total value of twenty-cent coins in the end
= 4 p x 20
= 4 x 7 x 20
= 560¢
Total value of ten-cent coins in the end
= 7 p x 10
= 7 x 7 x 10
= 490¢
Total value of the coins
= 560 + 490
= 1050¢
= $10.50
Answer(s): $10.50