If Emily gives Pierre $32, the amount of money she has will be 25% of his. If Pierre gives Emily $19, he will have the same amount of money as her. How much money did each of them have?
(a) Pierre
(b) Emily
|
Case 1 |
Case 2 |
|
Pierre |
Emily |
Pierre |
Emily |
Before |
4 u - 32 |
1 u + 32 |
2.5 u + 19 |
2.5 u - 19 |
Change |
+ 32 |
- 32 |
- 19 |
+ 19 |
After |
4 u |
1 u |
2.5 u |
2.5 u |
(a)
25% =
25100 =
14 In Case 1, when Emily gives to Pierre, there is an internal transfer of money from Emily to Pierre. The total amount that both have remains the same.
In Case 2, when Pierre gives to Emily, there is an internal transfer of money from Pierre to Emily. 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 Emily and Pierre have
= 4 u + 1 u
= 5 u
Amount that Emily and Pierre each has in the end for Case 2
= 5 u ÷ 2
= 2.5 u
Amount that Pierre has at first is the same in Case 1 and Case 2.
4 u - 32 = 2.5 u + 19
4 u - 2.5 u = 19 + 32
1.5 u = 51
1 u = 51 ÷ 1.5 = 34
Amount that Pierre has
= 4 u - 32
= 4 x 34 - 32
= 136 - 32
= $104
(b)
Amount that Emily has
= 1 u + 32
= 1 x 34 + 32
= 34 + 32
= $66
Answer(s): (a) $104; (b) $66