If Gwen gives Charlie $22, the amount of money she has will be 25% of his. If Charlie gives Gwen $29, he will have the same amount of money as her. How much money did each of them have?
(a) Charlie
(b) Gwen
|
Case 1 |
Case 2 |
|
Charlie |
Gwen |
Charlie |
Gwen |
Before |
4 u - 22 |
1 u + 22 |
2.5 u + 29 |
2.5 u - 29 |
Change |
+ 22 |
- 22 |
- 29 |
+ 29 |
After |
4 u |
1 u |
2.5 u |
2.5 u |
(a)
25% =
25100 =
14 In Case 1, when Gwen gives to Charlie, there is an internal transfer of money from Gwen to Charlie. The total amount that both have remains the same.
In Case 2, when Charlie gives to Gwen, there is an internal transfer of money from Charlie to Gwen. 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 Gwen and Charlie have
= 4 u + 1 u
= 5 u
Amount that Gwen and Charlie each has in the end for Case 2
= 5 u ÷ 2
= 2.5 u
Amount that Charlie has at first is the same in Case 1 and Case 2.
4 u - 22 = 2.5 u + 29
4 u - 2.5 u = 29 + 22
1.5 u = 51
1 u = 51 ÷ 1.5 = 34
Amount that Charlie has
= 4 u - 22
= 4 x 34 - 22
= 136 - 22
= $114
(b)
Amount that Gwen has
= 1 u + 22
= 1 x 34 + 22
= 34 + 22
= $56
Answer(s): (a) $114; (b) $56