If Anna gives Jenson $15, the amount of money she has will be 25% of his. If Jenson gives Anna $33, he will have the same amount of money as her. How much money did each of them have?
(a) Jenson
(b) Anna
|
Case 1 |
Case 2 |
|
Jenson |
Anna |
Jenson |
Anna |
Before |
4 u - 15 |
1 u + 15 |
2.5 u + 33 |
2.5 u - 33 |
Change |
+ 15 |
- 15 |
- 33 |
+ 33 |
After |
4 u |
1 u |
2.5 u |
2.5 u |
(a)
25% =
25100 =
14 In Case 1, when Anna gives to Jenson, there is an internal transfer of money from Anna to Jenson. The total amount that both have remains the same.
In Case 2, when Jenson gives to Anna, there is an internal transfer of money from Jenson to Anna. 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 Anna and Jenson have
= 4 u + 1 u
= 5 u
Amount that Anna and Jenson each has in the end for Case 2
= 5 u ÷ 2
= 2.5 u
Amount that Jenson has at first is the same in Case 1 and Case 2.
4 u - 15 = 2.5 u + 33
4 u - 2.5 u = 33 + 15
1.5 u = 48
1 u = 48 ÷ 1.5 = 32
Amount that Jenson has
= 4 u - 15
= 4 x 32 - 15
= 128 - 15
= $113
(b)
Amount that Anna has
= 1 u + 15
= 1 x 32 + 15
= 32 + 15
= $47
Answer(s): (a) $113; (b) $47