If Erika gives Xavier $25, the amount of money she has will be 25% of his. If Xavier gives Erika $29, he will have the same amount of money as her. How much money did each of them have?
(a) Xavier
(b) Erika
|
Case 1 |
Case 2 |
|
Xavier |
Erika |
Xavier |
Erika |
Before |
4 u - 25 |
1 u + 25 |
2.5 u + 29 |
2.5 u - 29 |
Change |
+ 25 |
- 25 |
- 29 |
+ 29 |
After |
4 u |
1 u |
2.5 u |
2.5 u |
(a)
25% =
25100 =
14 In Case 1, when Erika gives to Xavier, there is an internal transfer of money from Erika to Xavier. The total amount that both have remains the same.
In Case 2, when Xavier gives to Erika, there is an internal transfer of money from Xavier to Erika. 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 Erika and Xavier have
= 4 u + 1 u
= 5 u
Amount that Erika and Xavier each has in the end for Case 2
= 5 u ÷ 2
= 2.5 u
Amount that Xavier has at first is the same in Case 1 and Case 2.
4 u - 25 = 2.5 u + 29
4 u - 2.5 u = 29 + 25
1.5 u = 54
1 u = 54 ÷ 1.5 = 36
Amount that Xavier has
= 4 u - 25
= 4 x 36 - 25
= 144 - 25
= $119
(b)
Amount that Erika has
= 1 u + 25
= 1 x 36 + 25
= 36 + 25
= $61
Answer(s): (a) $119; (b) $61