If Linda gives Daniel $17, the amount of money she has will be 40% of his. If Daniel gives Linda $43, he will have the same amount of money as her. How much money did each of them have?
(a) Daniel
(b) Linda
|
Case 1 |
Case 2 |
|
Daniel |
Linda |
Daniel |
Linda |
Before |
5 u - 17 |
2 u + 17 |
3.5 u + 43 |
3.5 u - 43 |
Change |
+ 17 |
- 17 |
- 43 |
+ 43 |
After |
5 u |
2 u |
3.5 u |
3.5 u |
(a)
40% =
40100 =
25 In Case 1, when Linda gives to Daniel, there is an internal transfer of money from Linda to Daniel. The total amount that both have remains the same.
In Case 2, when Daniel gives to Linda, there is an internal transfer of money from Daniel to Linda. 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 Linda and Daniel have
= 5 u + 2 u
= 7 u
Amount that Linda and Daniel each has in the end for Case 2
= 7 u ÷ 2
= 3.5 u
Amount that Daniel has at first is the same in Case 1 and Case 2.
5 u - 17 = 3.5 u + 43
5 u - 3.5 u = 43 + 17
1.5 u = 60
1 u = 60 ÷ 1.5 = 40
Amount that Daniel has
= 5 u - 17
= 5 x 40 - 17
= 200 - 17
= $183
(b)
Amount that Linda has
= 2 u + 17
= 2 x 40 + 17
= 80 + 17
= $97
Answer(s): (a) $183; (b) $97