If Winnie gives Will $29, the amount of money she has will be 25% of his. If Will gives Winnie $16, he will have the same amount of money as her. How much money did each of them have?
(a) Will
(b) Winnie
|
Case 1 |
Case 2 |
|
Will |
Winnie |
Will |
Winnie |
Before |
4 u - 29 |
1 u + 29 |
2.5 u + 16 |
2.5 u - 16 |
Change |
+ 29 |
- 29 |
- 16 |
+ 16 |
After |
4 u |
1 u |
2.5 u |
2.5 u |
(a)
25% =
25100 =
14 In Case 1, when Winnie gives to Will, there is an internal transfer of money from Winnie to Will. The total amount that both have remains the same.
In Case 2, when Will gives to Winnie, there is an internal transfer of money from Will to Winnie. 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 Winnie and Will have
= 4 u + 1 u
= 5 u
Amount that Winnie and Will each has in the end for Case 2
= 5 u ÷ 2
= 2.5 u
Amount that Will has at first is the same in Case 1 and Case 2.
4 u - 29 = 2.5 u + 16
4 u - 2.5 u = 16 + 29
1.5 u = 45
1 u = 45 ÷ 1.5 = 30
Amount that Will has
= 4 u - 29
= 4 x 30 - 29
= 120 - 29
= $91
(b)
Amount that Winnie has
= 1 u + 29
= 1 x 30 + 29
= 30 + 29
= $59
Answer(s): (a) $91; (b) $59