If Gabby gives Bryan $32, the amount of money she has will be 40% of his. If Bryan gives Gabby $7, he will have the same amount of money as her. How much money did each of them have?
(a) Bryan
(b) Gabby
|
Case 1 |
Case 2 |
|
Bryan |
Gabby |
Bryan |
Gabby |
Before |
5 u - 32 |
2 u + 32 |
3.5 u + 7 |
3.5 u - 7 |
Change |
+ 32 |
- 32 |
- 7 |
+ 7 |
After |
5 u |
2 u |
3.5 u |
3.5 u |
(a)
40% =
40100 =
25 In Case 1, when Gabby gives to Bryan, there is an internal transfer of money from Gabby to Bryan. The total amount that both have remains the same.
In Case 2, when Bryan gives to Gabby, there is an internal transfer of money from Bryan to Gabby. 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 Gabby and Bryan have
= 5 u + 2 u
= 7 u
Amount that Gabby and Bryan each has in the end for Case 2
= 7 u ÷ 2
= 3.5 u
Amount that Bryan has at first is the same in Case 1 and Case 2.
5 u - 32 = 3.5 u + 7
5 u - 3.5 u = 7 + 32
1.5 u = 39
1 u = 39 ÷ 1.5 = 26
Amount that Bryan has
= 5 u - 32
= 5 x 26 - 32
= 130 - 32
= $98
(b)
Amount that Gabby has
= 2 u + 32
= 2 x 26 + 32
= 52 + 32
= $84
Answer(s): (a) $98; (b) $84