If Jack gives Jane $6, he will have the same amount of money as her. If Jane gives Jack $6, Jack will have four times as much money as her. How much money does Jane have?
| |
Scenario 1 |
Scenario 2 |
| |
Jack |
Jane |
Total |
Jack |
Jane |
Total |
| Before |
5 u + 6 |
5 u - 6 |
|
2 u - 6 |
8 u + 6 |
|
| Change |
- 6 |
+ 6 |
|
+ 6 |
- 6 |
|
| After |
1x5 =
5 u |
1x5 =
5 u |
2x5 =
10 u |
1x2 =
2 u |
4x2 =
8 u |
5x2 =
10 u |
The total amount in both scenarios is the same. LCM of 2 and 5 is 10.
In both scenarios, Jack had the same amount at first.
5 u + 6 = 2 u - 6
5 u - 2 u = 6 + 6
3 u = 12
1 u = 12 ÷ 3 = 4
Amount that Jane has
= 5 u - 6
= 5 x 4 - 6
= $14
Answer(s): $14
