If Olivia gives Xavier $14, the amount of money she has will be 30% of his. If Xavier gives Olivia $140, he will have the same amount of money as her. How much money did each of them have?
(a) Xavier
(b) Olivia
|
Case 1 |
Case 2 |
|
Xavier |
Olivia |
Xavier |
Olivia |
Before |
10 u - 14 |
3 u + 14 |
6.5 u + 140 |
6.5 u - 140 |
Change |
+ 14 |
- 14 |
- 140 |
+ 140 |
After |
10 u |
3 u |
6.5 u |
6.5 u |
(a)
30% =
30100 =
310 In Case 1, when Olivia gives to Xavier, there is an internal transfer of money from Olivia to Xavier. The total amount that both have remains the same.
In Case 2, when Xavier gives to Olivia, there is an internal transfer of money from Xavier to Olivia. 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 Olivia and Xavier have
= 10 u + 3 u
= 13 u
Amount that Olivia 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 - 14 = 6.5 u + 140
10 u - 6.5 u = 140 + 14
3.5 u = 154
1 u = 154 ÷ 3.5 = 44
Amount that Xavier has
= 10 u - 14
= 10 x 44 - 14
= 440 - 14
= $426
(b)
Amount that Olivia has
= 3 u + 14
= 3 x 44 + 14
= 132 + 14
= $146
Answer(s): (a) $426; (b) $146