Mark and Erika has some money each. If Erika gives Mark $14, he will have 3 times as much money as her. If Mark gives Erika $15, he will have the same amount of money as her. How much money does each person have respectively?
- Mark?
- Erika?
|
Case 1 |
Case 2 |
|
Mark |
Erika |
Mark |
Erika |
Before |
3 u - 14 |
1 u + 14 |
2 u + 15 |
2 u - 15 |
Change |
+ 14 |
- 14 |
- 15 |
+ 15 |
After |
3 u |
1 u |
2 u |
2 u |
(a)
If Erika gives Mark some money or Mark gives Erika some money, the total amount of money remains the same.
Total amount that Mark and Erika have in the end for both cases
= 3 u + 1 u
= 4 u
Amount that Mark and Erika each has in the end in Case 2
= 4 u ÷ 2
= 2 u
The amount that Mark has at first in Case 1 and Case 2 is the same.
3 u - 14 = 2 u + 15
3 u - 2 u = 15 + 14
1 u = 29
Amount that Mark has
= 2 u + 15
= 2 x 29 + 15
= 58 + 15
= $73
(b)
Amount that Erika has
= 1 u + 14
= 29 + 14
= $43
Answer(s): (a) $73; (b) $43