If Linda gives Xavier $40, the amount of money she has will be 25% of his. If Xavier gives Linda $5, he will have the same amount of money as her. How much money did each of them have?
(a) Xavier
(b) Linda
|
Case 1 |
Case 2 |
|
Xavier |
Linda |
Xavier |
Linda |
Before |
4 u - 40 |
1 u + 40 |
2.5 u + 5 |
2.5 u - 5 |
Change |
+ 40 |
- 40 |
- 5 |
+ 5 |
After |
4 u |
1 u |
2.5 u |
2.5 u |
(a)
25% =
25100 =
14 In Case 1, when Linda gives to Xavier, there is an internal transfer of money from Linda to Xavier. The total amount that both have remains the same.
In Case 2, when Xavier gives to Linda, there is an internal transfer of money from Xavier to Linda. The total amount that both have remains the same.
The total amount that both have in Case 1 and Case 2 are the same.
Total amount that Linda and Xavier have
= 4 u + 1 u
= 5 u
Amount that Linda and Xavier each has in the end for Case 2
= 5 u ÷ 2
= 2.5 u
Amount that Xavier has at first is the same in Case 1 and Case 2.
4 u - 40 = 2.5 u + 5
4 u - 2.5 u = 5 + 40
1.5 u = 45
1 u = 45 ÷ 1.5 = 30
Amount that Xavier has
= 4 u - 40
= 4 x 30 - 40
= 120 - 40
= $80
(b)
Amount that Linda has
= 1 u + 40
= 1 x 30 + 40
= 30 + 40
= $70
Answer(s): (a) $80; (b) $70