If Gabby gives Neave $26, the amount of money she has will be 40% of his. If Neave gives Gabby $13, he will have the same amount of money as her. How much money did each of them have?
(a) Neave
(b) Gabby
|
Case 1 |
Case 2 |
|
Neave |
Gabby |
Neave |
Gabby |
Before |
5 u - 26 |
2 u + 26 |
3.5 u + 13 |
3.5 u - 13 |
Change |
+ 26 |
- 26 |
- 13 |
+ 13 |
After |
5 u |
2 u |
3.5 u |
3.5 u |
(a)
40% =
40100 =
25 In Case 1, when Gabby gives to Neave, there is an internal transfer of money from Gabby to Neave. The total amount that both have remains the same.
In Case 2, when Neave gives to Gabby, there is an internal transfer of money from Neave 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 Neave have
= 5 u + 2 u
= 7 u
Amount that Gabby and Neave each has in the end for Case 2
= 7 u ÷ 2
= 3.5 u
Amount that Neave has at first is the same in Case 1 and Case 2.
5 u - 26 = 3.5 u + 13
5 u - 3.5 u = 13 + 26
1.5 u = 39
1 u = 39 ÷ 1.5 = 26
Amount that Neave has
= 5 u - 26
= 5 x 26 - 26
= 130 - 26
= $104
(b)
Amount that Gabby has
= 2 u + 26
= 2 x 26 + 26
= 52 + 26
= $78
Answer(s): (a) $104; (b) $78