If Sam gives Penelope $3, he will have the same amount of money as her. If Penelope gives Sam $3, Sam will have four times as much money as her. How much money does Penelope have?
| |
Scenario 1 |
Scenario 2 |
| |
Sam |
Penelope |
Total |
Sam |
Penelope |
Total |
| Before |
5 u + 3 |
5 u - 3 |
|
2 u - 3 |
8 u + 3 |
|
| Change |
- 3 |
+ 3 |
|
+ 3 |
- 3 |
|
| 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, Sam had the same amount at first.
5 u + 3 = 2 u - 3
5 u - 2 u = 3 + 3
3 u = 6
1 u = 6 ÷ 3 = 2
Amount that Penelope has
= 5 u - 3
= 5 x 2 - 3
= $7
Answer(s): $7
