If Xylia gives Sean $20, the amount of money she has will be 40% of his. If Sean gives Xylia $34, he will have the same amount of money as her. How much money did each of them have?
(a) Sean
(b) Xylia
|
Case 1 |
Case 2 |
|
Sean |
Xylia |
Sean |
Xylia |
Before |
5 u - 20 |
2 u + 20 |
3.5 u + 34 |
3.5 u - 34 |
Change |
+ 20 |
- 20 |
- 34 |
+ 34 |
After |
5 u |
2 u |
3.5 u |
3.5 u |
(a)
40% =
40100 =
25 In Case 1, when Xylia gives to Sean, there is an internal transfer of money from Xylia to Sean. The total amount that both have remains the same.
In Case 2, when Sean gives to Xylia, there is an internal transfer of money from Sean to Xylia. 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 Xylia and Sean have
= 5 u + 2 u
= 7 u
Amount that Xylia and Sean each has in the end for Case 2
= 7 u ÷ 2
= 3.5 u
Amount that Sean has at first is the same in Case 1 and Case 2.
5 u - 20 = 3.5 u + 34
5 u - 3.5 u = 34 + 20
1.5 u = 54
1 u = 54 ÷ 1.5 = 36
Amount that Sean has
= 5 u - 20
= 5 x 36 - 20
= 180 - 20
= $160
(b)
Amount that Xylia has
= 2 u + 20
= 2 x 36 + 20
= 72 + 20
= $92
Answer(s): (a) $160; (b) $92