If Roshel gives Xavier $21, the amount of money she has will be 40% of his. If Xavier gives Roshel $39, he will have the same amount of money as her. How much money did each of them have?
(a) Xavier
(b) Roshel
|
Case 1 |
Case 2 |
|
Xavier |
Roshel |
Xavier |
Roshel |
Before |
5 u - 21 |
2 u + 21 |
3.5 u + 39 |
3.5 u - 39 |
Change |
+ 21 |
- 21 |
- 39 |
+ 39 |
After |
5 u |
2 u |
3.5 u |
3.5 u |
(a)
40% =
40100 =
25 In Case 1, when Roshel gives to Xavier, there is an internal transfer of money from Roshel to Xavier. The total amount that both have remains the same.
In Case 2, when Xavier gives to Roshel, there is an internal transfer of money from Xavier to Roshel. 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 Roshel and Xavier have
= 5 u + 2 u
= 7 u
Amount that Roshel and Xavier each has in the end for Case 2
= 7 u ÷ 2
= 3.5 u
Amount that Xavier has at first is the same in Case 1 and Case 2.
5 u - 21 = 3.5 u + 39
5 u - 3.5 u = 39 + 21
1.5 u = 60
1 u = 60 ÷ 1.5 = 40
Amount that Xavier has
= 5 u - 21
= 5 x 40 - 21
= 200 - 21
= $179
(b)
Amount that Roshel has
= 2 u + 21
= 2 x 40 + 21
= 80 + 21
= $101
Answer(s): (a) $179; (b) $101