The number of twenty-cent coins in a bag was 300% 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
25 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)x4 = (3) |
| Before |
4 u |
1 u |
4 u |
| Change |
- 17 |
+ 34 |
+ 136 |
| After |
3 p |
5 p |
20 p |
100 + 300100=
400100 =
41 At first
Twenty-cent coins : Ten-cent coins
4 : 1
1 -
25 =
35 In the end
Twenty-cent coins : Ten-cent coins
3 : 5
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.
4 u - 17 = 3 p
4 u = 3 p + 17 --- (1)
1 u + 34 = 5 p --- (2)
(2)x4
4 u + 136 = 20 p
4 u = 20 p - 136 --- (3)
(3) = (1)
20 p - 136 = 3 p + 17
20 p - 3 p = 17 + 136
17 p = 153
1 p = 153 ÷ 17 = 9
The total value of the coins at first and in the end remains unchanged.
Total value of twenty-cent coins in the end
= 3 p x 20
= 3 x 9 x 20
= 540¢
Total value of ten-cent coins in the end
= 5 p x 10
= 5 x 9 x 10
= 450¢
Total value of the coins
= 540 + 450
= 990¢
= $9.90
Answer(s): $9.90
