If Kimberly gives Ken $24, the amount of money she has will be 25% of his. If Ken gives Kimberly $48, he will have the same amount of money as her. How much money did each of them have?
(a) Ken
(b) Kimberly
|
Case 1 |
Case 2 |
|
Ken |
Kimberly |
Ken |
Kimberly |
Before |
4 u - 24 |
1 u + 24 |
2.5 u + 48 |
2.5 u - 48 |
Change |
+ 24 |
- 24 |
- 48 |
+ 48 |
After |
4 u |
1 u |
2.5 u |
2.5 u |
(a)
25% =
25100 =
14 In Case 1, when Kimberly gives to Ken, there is an internal transfer of money from Kimberly to Ken. The total amount that both have remains the same.
In Case 2, when Ken gives to Kimberly, there is an internal transfer of money from Ken to Kimberly. 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 Kimberly and Ken have
= 4 u + 1 u
= 5 u
Amount that Kimberly and Ken each has in the end for Case 2
= 5 u ÷ 2
= 2.5 u
Amount that Ken has at first is the same in Case 1 and Case 2.
4 u - 24 = 2.5 u + 48
4 u - 2.5 u = 48 + 24
1.5 u = 72
1 u = 72 ÷ 1.5 = 48
Amount that Ken has
= 4 u - 24
= 4 x 48 - 24
= 192 - 24
= $168
(b)
Amount that Kimberly has
= 1 u + 24
= 1 x 48 + 24
= 48 + 24
= $72
Answer(s): (a) $168; (b) $72