If Joelle gives Xavier $25, the amount of money she has will be 25% of his. If Xavier gives Joelle $14, he will have the same amount of money as her. How much money did each of them have?
(a) Xavier
(b) Joelle
|
Case 1 |
Case 2 |
|
Xavier |
Joelle |
Xavier |
Joelle |
Before |
4 u - 25 |
1 u + 25 |
2.5 u + 14 |
2.5 u - 14 |
Change |
+ 25 |
- 25 |
- 14 |
+ 14 |
After |
4 u |
1 u |
2.5 u |
2.5 u |
(a)
25% =
25100 =
14 In Case 1, when Joelle gives to Xavier, there is an internal transfer of money from Joelle to Xavier. The total amount that both have remains the same.
In Case 2, when Xavier gives to Joelle, there is an internal transfer of money from Xavier to Joelle. 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 Joelle and Xavier have
= 4 u + 1 u
= 5 u
Amount that Joelle 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 + 14
4 u - 2.5 u = 14 + 25
1.5 u = 39
1 u = 39 ÷ 1.5 = 26
Amount that Xavier has
= 4 u - 25
= 4 x 26 - 25
= 104 - 25
= $79
(b)
Amount that Joelle has
= 1 u + 25
= 1 x 26 + 25
= 26 + 25
= $51
Answer(s): (a) $79; (b) $51