If Elyse gives Sean $17, the amount of money she has will be 25% of his. If Sean gives Elyse $58, he will have the same amount of money as her. How much money did each of them have?
(a) Sean
(b) Elyse
|
Case 1 |
Case 2 |
|
Sean |
Elyse |
Sean |
Elyse |
Before |
4 u - 17 |
1 u + 17 |
2.5 u + 58 |
2.5 u - 58 |
Change |
+ 17 |
- 17 |
- 58 |
+ 58 |
After |
4 u |
1 u |
2.5 u |
2.5 u |
(a)
25% =
25100 =
14 In Case 1, when Elyse gives to Sean, there is an internal transfer of money from Elyse to Sean. The total amount that both have remains the same.
In Case 2, when Sean gives to Elyse, there is an internal transfer of money from Sean to Elyse. 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 Elyse and Sean have
= 4 u + 1 u
= 5 u
Amount that Elyse and Sean each has in the end for Case 2
= 5 u ÷ 2
= 2.5 u
Amount that Sean has at first is the same in Case 1 and Case 2.
4 u - 17 = 2.5 u + 58
4 u - 2.5 u = 58 + 17
1.5 u = 75
1 u = 75 ÷ 1.5 = 50
Amount that Sean has
= 4 u - 17
= 4 x 50 - 17
= 200 - 17
= $183
(b)
Amount that Elyse has
= 1 u + 17
= 1 x 50 + 17
= 50 + 17
= $67
Answer(s): (a) $183; (b) $67