If Eva gives Luke $23, the amount of money she has will be 30% of his. If Luke gives Eva $82, he will have the same amount of money as her. How much money did each of them have?
(a) Luke
(b) Eva
|
Case 1 |
Case 2 |
|
Luke |
Eva |
Luke |
Eva |
Before |
10 u - 23 |
3 u + 23 |
6.5 u + 82 |
6.5 u - 82 |
Change |
+ 23 |
- 23 |
- 82 |
+ 82 |
After |
10 u |
3 u |
6.5 u |
6.5 u |
(a)
30% =
30100 =
310 In Case 1, when Eva gives to Luke, there is an internal transfer of money from Eva to Luke. The total amount that both have remains the same.
In Case 2, when Luke gives to Eva, there is an internal transfer of money from Luke 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 Luke have
= 10 u + 3 u
= 13 u
Amount that Eva and Luke each has in the end for Case 2
= 13 u ÷ 2
= 6.5 u
Amount that Luke has at first is the same in Case 1 and Case 2.
10 u - 23 = 6.5 u + 82
10 u - 6.5 u = 82 + 23
3.5 u = 105
1 u = 105 ÷ 3.5 = 30
Amount that Luke has
= 10 u - 23
= 10 x 30 - 23
= 300 - 23
= $277
(b)
Amount that Eva has
= 3 u + 23
= 3 x 30 + 23
= 90 + 23
= $113
Answer(s): (a) $277; (b) $113