If Fred gives Betty $7, he will have the same amount of money as her. If Betty gives Fred $7, Fred will have five times as much money as her. How much money does Betty have?
| |
Scenario 1 |
Scenario 2 |
| |
Fred |
Betty |
Total |
Fred |
Betty |
Total |
| Before |
3 u + 7 |
3 u - 7 |
|
1 u - 7 |
5 u + 7 |
|
| Change |
- 7 |
+ 7 |
|
+ 7 |
- 7 |
|
| 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, Fred had the same amount at first.
3 u + 7 = 1 u - 7
3 u - 1 u = 7 + 7
2 u = 14
1 u = 14 ÷ 2 = 7
Amount that Betty has
= 3 u - 7
= 3 x 7 - 7
= $14
Answer(s): $14
