If Julian gives Opal $2, he will have the same amount of money as her. If Opal gives Julian $2, Julian will have five times as much money as her. How much money does Opal have?
| |
Scenario 1 |
Scenario 2 |
| |
Julian |
Opal |
Total |
Julian |
Opal |
Total |
| Before |
3 u + 2 |
3 u - 2 |
|
1 u - 2 |
5 u + 2 |
|
| Change |
- 2 |
+ 2 |
|
+ 2 |
- 2 |
|
| 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, Julian had the same amount at first.
3 u + 2 = 1 u - 2
3 u - 1 u = 2 + 2
2 u = 4
1 u = 4 ÷ 2 = 2
Amount that Opal has
= 3 u - 2
= 3 x 2 - 2
= $4
Answer(s): $4
