If Dylan gives Rachel $6, he will have the same amount of money as her. If Rachel gives Dylan $6, Dylan will have five times as much money as her. How much money does Rachel have?
| |
Scenario 1 |
Scenario 2 |
| |
Dylan |
Rachel |
Total |
Dylan |
Rachel |
Total |
| Before |
3 u + 6 |
3 u - 6 |
|
1 u - 6 |
5 u + 6 |
|
| Change |
- 6 |
+ 6 |
|
+ 6 |
- 6 |
|
| 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, Dylan had the same amount at first.
3 u + 6 = 1 u - 6
3 u - 1 u = 6 + 6
2 u = 12
1 u = 12 ÷ 2 = 6
Amount that Rachel has
= 3 u - 6
= 3 x 6 - 6
= $12
Answer(s): $12
