George and Linda has some money each. If Linda gives George $17, he will have 3 times as much money as her. If George gives Linda $11, he will have the same amount of money as her. How much money does each person have respectively?
- George?
- Linda?
| |
Case 1 |
Case 2 |
| |
George |
Linda |
George |
Linda |
| Before |
3 u - 17 |
1 u + 17 |
2 u + 11 |
2 u - 11 |
| Change |
+ 17 |
- 17 |
- 11 |
+ 11 |
| After |
3 u |
1 u |
2 u |
2 u |
(a)
If Linda gives George some money or George gives Linda some money, the total amount of money remains the same.
Total amount that George and Linda have in the end for both cases
= 3 u + 1 u
= 4 u
Amount that George and Linda each has in the end in Case 2
= 4 u ÷ 2
= 2 u
The amount that George has at first in Case 1 and Case 2 is the same.
3 u - 17 = 2 u + 11
3 u - 2 u = 11 + 17
1 u = 28
Amount that George has
= 2 u + 11
= 2 x 28 + 11
= 56 + 11
= $67
(b)
Amount that Linda has
= 1 u + 17
= 28 + 17
= $45
Answer(s): (a) $67; (b) $45
