If Sabrina gives Ben $25, the amount of money she has will be 25% of his. If Ben gives Sabrina $32, he will have the same amount of money as her. How much money did each of them have?
(a) Ben
(b) Sabrina
|
Case 1 |
Case 2 |
|
Ben |
Sabrina |
Ben |
Sabrina |
Before |
4 u - 25 |
1 u + 25 |
2.5 u + 32 |
2.5 u - 32 |
Change |
+ 25 |
- 25 |
- 32 |
+ 32 |
After |
4 u |
1 u |
2.5 u |
2.5 u |
(a)
25% =
25100 =
14 In Case 1, when Sabrina gives to Ben, there is an internal transfer of money from Sabrina to Ben. The total amount that both have remains the same.
In Case 2, when Ben gives to Sabrina, there is an internal transfer of money from Ben 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 Ben have
= 4 u + 1 u
= 5 u
Amount that Sabrina and Ben each has in the end for Case 2
= 5 u ÷ 2
= 2.5 u
Amount that Ben has at first is the same in Case 1 and Case 2.
4 u - 25 = 2.5 u + 32
4 u - 2.5 u = 32 + 25
1.5 u = 57
1 u = 57 ÷ 1.5 = 38
Amount that Ben has
= 4 u - 25
= 4 x 38 - 25
= 152 - 25
= $127
(b)
Amount that Sabrina has
= 1 u + 25
= 1 x 38 + 25
= 38 + 25
= $63
Answer(s): (a) $127; (b) $63