If Kathy gives Fabian $32, the amount of money she has will be 10% of his. If Fabian gives Kathy $76, he will have the same amount of money as her. How much money did each of them have?
(a) Fabian
(b) Kathy
|
Case 1 |
Case 2 |
|
Fabian |
Kathy |
Fabian |
Kathy |
Before |
10 u - 32 |
1 u + 32 |
5.5 u + 76 |
5.5 u - 76 |
Change |
+ 32 |
- 32 |
- 76 |
+ 76 |
After |
10 u |
1 u |
5.5 u |
5.5 u |
(a)
10% =
10100 =
110 In Case 1, when Kathy gives to Fabian, there is an internal transfer of money from Kathy to Fabian. The total amount that both have remains the same.
In Case 2, when Fabian gives to Kathy, there is an internal transfer of money from Fabian to Kathy. 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 Kathy and Fabian have
= 10 u + 1 u
= 11 u
Amount that Kathy and Fabian each has in the end for Case 2
= 11 u ÷ 2
= 5.5 u
Amount that Fabian has at first is the same in Case 1 and Case 2.
10 u - 32 = 5.5 u + 76
10 u - 5.5 u = 76 + 32
4.5 u = 108
1 u = 108 ÷ 4.5 = 24
Amount that Fabian has
= 10 u - 32
= 10 x 24 - 32
= 240 - 32
= $208
(b)
Amount that Kathy has
= 1 u + 32
= 1 x 24 + 32
= 24 + 32
= $56
Answer(s): (a) $208; (b) $56