Henry and Jen has some money each. If Jen gives Henry $20, he will have 3 times as much money as her. If Henry gives Jen $14, he will have the same amount of money as her. How much money does each person have respectively?
- Henry?
- Jen?
|
Case 1 |
Case 2 |
|
Henry |
Jen |
Henry |
Jen |
Before |
3 u - 20 |
1 u + 20 |
2 u + 14 |
2 u - 14 |
Change |
+ 20 |
- 20 |
- 14 |
+ 14 |
After |
3 u |
1 u |
2 u |
2 u |
(a)
If Jen gives Henry some money or Henry gives Jen some money, the total amount of money remains the same.
Total amount that Henry and Jen have in the end for both cases
= 3 u + 1 u
= 4 u
Amount that Henry and Jen each has in the end in Case 2
= 4 u ÷ 2
= 2 u
The amount that Henry has at first in Case 1 and Case 2 is the same.
3 u - 20 = 2 u + 14
3 u - 2 u = 14 + 20
1 u = 34
Amount that Henry has
= 2 u + 14
= 2 x 34 + 14
= 68 + 14
= $82
(b)
Amount that Jen has
= 1 u + 20
= 34 + 20
= $54
Answer(s): (a) $82; (b) $54