If Anna gives Pierre $26, the amount of money she has will be 40% of his. If Pierre gives Anna $13, he will have the same amount of money as her. How much money did each of them have?
(a) Pierre
(b) Anna
|
Case 1 |
Case 2 |
|
Pierre |
Anna |
Pierre |
Anna |
Before |
5 u - 26 |
2 u + 26 |
3.5 u + 13 |
3.5 u - 13 |
Change |
+ 26 |
- 26 |
- 13 |
+ 13 |
After |
5 u |
2 u |
3.5 u |
3.5 u |
(a)
40% =
40100 =
25 In Case 1, when Anna gives to Pierre, there is an internal transfer of money from Anna to Pierre. The total amount that both have remains the same.
In Case 2, when Pierre gives to Anna, there is an internal transfer of money from Pierre 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 Pierre have
= 5 u + 2 u
= 7 u
Amount that Anna and Pierre each has in the end for Case 2
= 7 u ÷ 2
= 3.5 u
Amount that Pierre has at first is the same in Case 1 and Case 2.
5 u - 26 = 3.5 u + 13
5 u - 3.5 u = 13 + 26
1.5 u = 39
1 u = 39 ÷ 1.5 = 26
Amount that Pierre has
= 5 u - 26
= 5 x 26 - 26
= 130 - 26
= $104
(b)
Amount that Anna has
= 2 u + 26
= 2 x 26 + 26
= 52 + 26
= $78
Answer(s): (a) $104; (b) $78