If Peter gives Gwen $8, he will have the same amount of money as her. If Gwen gives Peter $8, Peter will have five times as much money as her. How much money does Gwen have?
| |
Scenario 1 |
Scenario 2 |
| |
Peter |
Gwen |
Total |
Peter |
Gwen |
Total |
| Before |
3 u + 8 |
3 u - 8 |
|
1 u - 8 |
5 u + 8 |
|
| Change |
- 8 |
+ 8 |
|
+ 8 |
- 8 |
|
| After |
1x3 =
3 u |
1x3 =
3 u |
2x3 =
6 u |
1x1 =
1 u |
5x1 =
5 u |
6x1 =
6 u |
The total amount in both scenarios is the same. LCM of 2 and 6 is 6.
In both scenarios, Peter had the same amount at first.
3 u + 8 = 1 u - 8
3 u - 1 u = 8 + 8
2 u = 16
1 u = 16 ÷ 2 = 8
Amount that Gwen has
= 3 u - 8
= 3 x 8 - 8
= $16
Answer(s): $16
