If Penelope gives Jenson $35, the amount of money she has will be 30% of his. If Jenson gives Penelope $119, he will have the same amount of money as her. How much money did each of them have?
(a) Jenson
(b) Penelope
|
Case 1 |
Case 2 |
|
Jenson |
Penelope |
Jenson |
Penelope |
Before |
10 u - 35 |
3 u + 35 |
6.5 u + 119 |
6.5 u - 119 |
Change |
+ 35 |
- 35 |
- 119 |
+ 119 |
After |
10 u |
3 u |
6.5 u |
6.5 u |
(a)
30% =
30100 =
310 In Case 1, when Penelope gives to Jenson, there is an internal transfer of money from Penelope to Jenson. The total amount that both have remains the same.
In Case 2, when Jenson gives to Penelope, there is an internal transfer of money from Jenson 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 Jenson have
= 10 u + 3 u
= 13 u
Amount that Penelope and Jenson each has in the end for Case 2
= 13 u ÷ 2
= 6.5 u
Amount that Jenson has at first is the same in Case 1 and Case 2.
10 u - 35 = 6.5 u + 119
10 u - 6.5 u = 119 + 35
3.5 u = 154
1 u = 154 ÷ 3.5 = 44
Amount that Jenson has
= 10 u - 35
= 10 x 44 - 35
= 440 - 35
= $405
(b)
Amount that Penelope has
= 3 u + 35
= 3 x 44 + 35
= 132 + 35
= $167
Answer(s): (a) $405; (b) $167