If Ben gives Jane $5, he will have the same amount of money as her. If Jane gives Ben $5, Ben will have five times as much money as her. How much money does Jane have?
| |
Scenario 1 |
Scenario 2 |
| |
Ben |
Jane |
Total |
Ben |
Jane |
Total |
| Before |
3 u + 5 |
3 u - 5 |
|
1 u - 5 |
5 u + 5 |
|
| Change |
- 5 |
+ 5 |
|
+ 5 |
- 5 |
|
| 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, Ben had the same amount at first.
3 u + 5 = 1 u - 5
3 u - 1 u = 5 + 5
2 u = 10
1 u = 10 ÷ 2 = 5
Amount that Jane has
= 3 u - 5
= 3 x 5 - 5
= $10
Answer(s): $10
