If Jean gives Xavier $17, the amount of money she has will be 30% of his. If Xavier gives Jean $116, he will have the same amount of money as her. How much money did each of them have?
(a) Xavier
(b) Jean
|
Case 1 |
Case 2 |
|
Xavier |
Jean |
Xavier |
Jean |
Before |
10 u - 17 |
3 u + 17 |
6.5 u + 116 |
6.5 u - 116 |
Change |
+ 17 |
- 17 |
- 116 |
+ 116 |
After |
10 u |
3 u |
6.5 u |
6.5 u |
(a)
30% =
30100 =
310 In Case 1, when Jean gives to Xavier, there is an internal transfer of money from Jean to Xavier. The total amount that both have remains the same.
In Case 2, when Xavier gives to Jean, there is an internal transfer of money from Xavier to Jean. 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 Jean and Xavier have
= 10 u + 3 u
= 13 u
Amount that Jean and Xavier each has in the end for Case 2
= 13 u ÷ 2
= 6.5 u
Amount that Xavier has at first is the same in Case 1 and Case 2.
10 u - 17 = 6.5 u + 116
10 u - 6.5 u = 116 + 17
3.5 u = 133
1 u = 133 ÷ 3.5 = 38
Amount that Xavier has
= 10 u - 17
= 10 x 38 - 17
= 380 - 17
= $363
(b)
Amount that Jean has
= 3 u + 17
= 3 x 38 + 17
= 114 + 17
= $131
Answer(s): (a) $363; (b) $131