If Penelope gives Oscar $26, the amount of money she has will be 25% of his. If Oscar gives Penelope $25, he will have the same amount of money as her. How much money did each of them have?
(a) Oscar
(b) Penelope
|
Case 1 |
Case 2 |
|
Oscar |
Penelope |
Oscar |
Penelope |
Before |
4 u - 26 |
1 u + 26 |
2.5 u + 25 |
2.5 u - 25 |
Change |
+ 26 |
- 26 |
- 25 |
+ 25 |
After |
4 u |
1 u |
2.5 u |
2.5 u |
(a)
25% =
25100 =
14 In Case 1, when Penelope gives to Oscar, there is an internal transfer of money from Penelope to Oscar. The total amount that both have remains the same.
In Case 2, when Oscar gives to Penelope, there is an internal transfer of money from Oscar to Penelope. 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 Penelope and Oscar have
= 4 u + 1 u
= 5 u
Amount that Penelope and Oscar each has in the end for Case 2
= 5 u ÷ 2
= 2.5 u
Amount that Oscar has at first is the same in Case 1 and Case 2.
4 u - 26 = 2.5 u + 25
4 u - 2.5 u = 25 + 26
1.5 u = 51
1 u = 51 ÷ 1.5 = 34
Amount that Oscar has
= 4 u - 26
= 4 x 34 - 26
= 136 - 26
= $110
(b)
Amount that Penelope has
= 1 u + 26
= 1 x 34 + 26
= 34 + 26
= $60
Answer(s): (a) $110; (b) $60