Mark and Jen has some money each. If Jen gives Mark $20, he will have 7 times as much money as her. If Mark gives Jen $12, he will have the same amount of money as her. How much money does each person have respectively?
- Mark?
- Jen?
|
Case 1 |
Case 2 |
|
Mark |
Jen |
Mark |
Jen |
Before |
7 u - 20 |
1 u + 20 |
4 u + 12 |
4 u - 12 |
Change |
+ 20 |
- 20 |
- 12 |
+ 12 |
After |
7 u |
1 u |
4 u |
4 u |
(a)
If Jen gives Mark some money or Mark gives Jen some money, the total amount of money remains the same.
Total amount that Mark and Jen have in the end for both cases
= 7 u + 1 u
= 8 u
Amount that Mark and Jen each has in the end in Case 2
= 8 u ÷ 2
= 4 u
The amount that Mark has at first in Case 1 and Case 2 is the same.
7 u - 20 = 4 u + 12
7 u - 4 u = 12 + 20
1 u = 32
Amount that Mark has
= 4 u + 12
= 4 x 32 + 12
= 128 + 12
= $140
(b)
Amount that Jen has
= 1 u + 20
= 32 + 20
= $52
Answer(s): (a) $140; (b) $52