If Lynn gives Mark $20, the amount of money she has will be 25% of his. If Mark gives Lynn $34, he will have the same amount of money as her. How much money did each of them have?
(a) Mark
(b) Lynn
|
Case 1 |
Case 2 |
|
Mark |
Lynn |
Mark |
Lynn |
Before |
4 u - 20 |
1 u + 20 |
2.5 u + 34 |
2.5 u - 34 |
Change |
+ 20 |
- 20 |
- 34 |
+ 34 |
After |
4 u |
1 u |
2.5 u |
2.5 u |
(a)
25% =
25100 =
14 In Case 1, when Lynn gives to Mark, there is an internal transfer of money from Lynn to Mark. The total amount that both have remains the same.
In Case 2, when Mark gives to Lynn, there is an internal transfer of money from Mark to Lynn. 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 Lynn and Mark have
= 4 u + 1 u
= 5 u
Amount that Lynn and Mark each has in the end for Case 2
= 5 u ÷ 2
= 2.5 u
Amount that Mark has at first is the same in Case 1 and Case 2.
4 u - 20 = 2.5 u + 34
4 u - 2.5 u = 34 + 20
1.5 u = 54
1 u = 54 ÷ 1.5 = 36
Amount that Mark has
= 4 u - 20
= 4 x 36 - 20
= 144 - 20
= $124
(b)
Amount that Lynn has
= 1 u + 20
= 1 x 36 + 20
= 36 + 20
= $56
Answer(s): (a) $124; (b) $56