If Sabrina gives Wesley $26, the amount of money she has will be 25% of his. If Wesley gives Sabrina $4, he will have the same amount of money as her. How much money did each of them have?
(a) Wesley
(b) Sabrina
|
Case 1 |
Case 2 |
|
Wesley |
Sabrina |
Wesley |
Sabrina |
Before |
4 u - 26 |
1 u + 26 |
2.5 u + 4 |
2.5 u - 4 |
Change |
+ 26 |
- 26 |
- 4 |
+ 4 |
After |
4 u |
1 u |
2.5 u |
2.5 u |
(a)
25% =
25100 =
14 In Case 1, when Sabrina gives to Wesley, there is an internal transfer of money from Sabrina to Wesley. The total amount that both have remains the same.
In Case 2, when Wesley gives to Sabrina, there is an internal transfer of money from Wesley to Sabrina. 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 Sabrina and Wesley have
= 4 u + 1 u
= 5 u
Amount that Sabrina and Wesley each has in the end for Case 2
= 5 u ÷ 2
= 2.5 u
Amount that Wesley has at first is the same in Case 1 and Case 2.
4 u - 26 = 2.5 u + 4
4 u - 2.5 u = 4 + 26
1.5 u = 30
1 u = 30 ÷ 1.5 = 20
Amount that Wesley has
= 4 u - 26
= 4 x 20 - 26
= 80 - 26
= $54
(b)
Amount that Sabrina has
= 1 u + 26
= 1 x 20 + 26
= 20 + 26
= $46
Answer(s): (a) $54; (b) $46