If Eva gives Sam $19, the amount of money she has will be 40% of his. If Sam gives Eva $41, he will have the same amount of money as her. How much money did each of them have?
(a) Sam
(b) Eva
|
Case 1 |
Case 2 |
|
Sam |
Eva |
Sam |
Eva |
Before |
5 u - 19 |
2 u + 19 |
3.5 u + 41 |
3.5 u - 41 |
Change |
+ 19 |
- 19 |
- 41 |
+ 41 |
After |
5 u |
2 u |
3.5 u |
3.5 u |
(a)
40% =
40100 =
25 In Case 1, when Eva gives to Sam, there is an internal transfer of money from Eva to Sam. The total amount that both have remains the same.
In Case 2, when Sam gives to Eva, there is an internal transfer of money from Sam 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 Sam have
= 5 u + 2 u
= 7 u
Amount that Eva and Sam each has in the end for Case 2
= 7 u ÷ 2
= 3.5 u
Amount that Sam has at first is the same in Case 1 and Case 2.
5 u - 19 = 3.5 u + 41
5 u - 3.5 u = 41 + 19
1.5 u = 60
1 u = 60 ÷ 1.5 = 40
Amount that Sam has
= 5 u - 19
= 5 x 40 - 19
= 200 - 19
= $181
(b)
Amount that Eva has
= 2 u + 19
= 2 x 40 + 19
= 80 + 19
= $99
Answer(s): (a) $181; (b) $99