If Eva gives Charlie $38, the amount of money she has will be 40% of his. If Charlie gives Eva $1, he will have the same amount of money as her. How much money did each of them have?
(a) Charlie
(b) Eva
|
Case 1 |
Case 2 |
|
Charlie |
Eva |
Charlie |
Eva |
Before |
5 u - 38 |
2 u + 38 |
3.5 u + 1 |
3.5 u - 1 |
Change |
+ 38 |
- 38 |
- 1 |
+ 1 |
After |
5 u |
2 u |
3.5 u |
3.5 u |
(a)
40% =
40100 =
25 In Case 1, when Eva gives to Charlie, there is an internal transfer of money from Eva to Charlie. The total amount that both have remains the same.
In Case 2, when Charlie gives to Eva, there is an internal transfer of money from Charlie to Eva. 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 Eva and Charlie have
= 5 u + 2 u
= 7 u
Amount that Eva and Charlie each has in the end for Case 2
= 7 u ÷ 2
= 3.5 u
Amount that Charlie has at first is the same in Case 1 and Case 2.
5 u - 38 = 3.5 u + 1
5 u - 3.5 u = 1 + 38
1.5 u = 39
1 u = 39 ÷ 1.5 = 26
Amount that Charlie has
= 5 u - 38
= 5 x 26 - 38
= 130 - 38
= $92
(b)
Amount that Eva has
= 2 u + 38
= 2 x 26 + 38
= 52 + 38
= $90
Answer(s): (a) $92; (b) $90