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