If Fred gives Betty $5, he will have the same amount of money as her. If Betty gives Fred $5, Fred will have five times as much money as her. How much money does Fred have?
| |
Case 1 |
Case 2 |
| |
Fred |
Betty |
Fred |
Betty |
| Before |
3 u + 5 |
3 u - 5 |
1 u - 5 |
5 u + 5 |
| Change |
- 5 |
+ 5 |
+ 5 |
- 5 |
| 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, Fred had the same amount at first.
3 u + 5 = 1 u - 5
3 u - 1 u = 5 + 5
2 u = 10
1 u = 10 ÷ 2 = 5
Amount that Fred has
= 3 u + 5
= 3 x 5 + 5
= $20
Answer(s): $20
