If Eva gives Neave $17, the amount of money she has will be 40% of his. If Neave gives Eva $13, he will have the same amount of money as her. How much money did each of them have?
(a) Neave
(b) Eva
|
Case 1 |
Case 2 |
|
Neave |
Eva |
Neave |
Eva |
Before |
5 u - 17 |
2 u + 17 |
3.5 u + 13 |
3.5 u - 13 |
Change |
+ 17 |
- 17 |
- 13 |
+ 13 |
After |
5 u |
2 u |
3.5 u |
3.5 u |
(a)
40% =
40100 =
25 In Case 1, when Eva gives to Neave, there is an internal transfer of money from Eva to Neave. The total amount that both have remains the same.
In Case 2, when Neave gives to Eva, there is an internal transfer of money from Neave 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 Neave have
= 5 u + 2 u
= 7 u
Amount that Eva and Neave each has in the end for Case 2
= 7 u ÷ 2
= 3.5 u
Amount that Neave has at first is the same in Case 1 and Case 2.
5 u - 17 = 3.5 u + 13
5 u - 3.5 u = 13 + 17
1.5 u = 30
1 u = 30 ÷ 1.5 = 20
Amount that Neave has
= 5 u - 17
= 5 x 20 - 17
= 100 - 17
= $83
(b)
Amount that Eva has
= 2 u + 17
= 2 x 20 + 17
= 40 + 17
= $57
Answer(s): (a) $83; (b) $57