If Eva gives Peter $21, the amount of money she has will be 75% of his. If Peter gives Eva $3, he will have the same amount of money as her. How much money did each of them have?
(a) Peter
(b) Eva
|
Case 1 |
Case 2 |
|
Peter |
Eva |
Peter |
Eva |
Before |
4 u - 21 |
3 u + 21 |
3.5 u + 3 |
3.5 u - 3 |
Change |
+ 21 |
- 21 |
- 3 |
+ 3 |
After |
4 u |
3 u |
3.5 u |
3.5 u |
(a)
75% =
75100 =
34 In Case 1, when Eva gives to Peter, there is an internal transfer of money from Eva to Peter. The total amount that both have remains the same.
In Case 2, when Peter gives to Eva, there is an internal transfer of money from Peter to Eva. 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 Eva and Peter have
= 4 u + 3 u
= 7 u
Amount that Eva and Peter each has in the end for Case 2
= 7 u ÷ 2
= 3.5 u
Amount that Peter has at first is the same in Case 1 and Case 2.
4 u - 21 = 3.5 u + 3
4 u - 3.5 u = 3 + 21
0.5 u = 24
1 u = 24 ÷ 0.5 = 48
Amount that Peter has
= 4 u - 21
= 4 x 48 - 21
= 192 - 21
= $171
(b)
Amount that Eva has
= 3 u + 21
= 3 x 48 + 21
= 144 + 21
= $165
Answer(s): (a) $171; (b) $165