If Olivia gives Sean $38, the amount of money she has will be 30% of his. If Sean gives Olivia $102, he will have the same amount of money as her. How much money did each of them have?
(a) Sean
(b) Olivia
|
Case 1 |
Case 2 |
|
Sean |
Olivia |
Sean |
Olivia |
Before |
10 u - 38 |
3 u + 38 |
6.5 u + 102 |
6.5 u - 102 |
Change |
+ 38 |
- 38 |
- 102 |
+ 102 |
After |
10 u |
3 u |
6.5 u |
6.5 u |
(a)
30% =
30100 =
310 In Case 1, when Olivia gives to Sean, there is an internal transfer of money from Olivia to Sean. The total amount that both have remains the same.
In Case 2, when Sean gives to Olivia, there is an internal transfer of money from Sean 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 Sean have
= 10 u + 3 u
= 13 u
Amount that Olivia and Sean each has in the end for Case 2
= 13 u ÷ 2
= 6.5 u
Amount that Sean has at first is the same in Case 1 and Case 2.
10 u - 38 = 6.5 u + 102
10 u - 6.5 u = 102 + 38
3.5 u = 140
1 u = 140 ÷ 3.5 = 40
Amount that Sean has
= 10 u - 38
= 10 x 40 - 38
= 400 - 38
= $362
(b)
Amount that Olivia has
= 3 u + 38
= 3 x 40 + 38
= 120 + 38
= $158
Answer(s): (a) $362; (b) $158