If Luke gives Anna $3, he will have the same amount of money as her. If Anna gives Luke $3, Luke will have five times as much money as her. How much money does Luke have?
| |
Case 1 |
Case 2 |
| |
Luke |
Anna |
Luke |
Anna |
| 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 |
1x1 =
1 u |
5x1 =
5 u |
The total amount in both scenarios is the same. Make the total amount the same in bothe cases. LCM of 2 and 6 is 6.
In both case, Luke 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 Luke has
= 3 u + 3
= 3 x 3 + 3
= $12
Answer(s): $12
