If Gabby gives Zane $18, the amount of money she has will be 25% of his. If Zane gives Gabby $18, he will have the same amount of money as her. How much money did each of them have?
(a) Zane
(b) Gabby
|
Case 1 |
Case 2 |
|
Zane |
Gabby |
Zane |
Gabby |
Before |
4 u - 18 |
1 u + 18 |
2.5 u + 18 |
2.5 u - 18 |
Change |
+ 18 |
- 18 |
- 18 |
+ 18 |
After |
4 u |
1 u |
2.5 u |
2.5 u |
(a)
25% =
25100 =
14 In Case 1, when Gabby gives to Zane, there is an internal transfer of money from Gabby to Zane. The total amount that both have remains the same.
In Case 2, when Zane gives to Gabby, there is an internal transfer of money from Zane 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 Zane have
= 4 u + 1 u
= 5 u
Amount that Gabby and Zane each has in the end for Case 2
= 5 u ÷ 2
= 2.5 u
Amount that Zane has at first is the same in Case 1 and Case 2.
4 u - 18 = 2.5 u + 18
4 u - 2.5 u = 18 + 18
1.5 u = 36
1 u = 36 ÷ 1.5 = 24
Amount that Zane has
= 4 u - 18
= 4 x 24 - 18
= 96 - 18
= $78
(b)
Amount that Gabby has
= 1 u + 18
= 1 x 24 + 18
= 24 + 18
= $42
Answer(s): (a) $78; (b) $42