Harry and Jen has some money each. If Jen gives Harry $11, he will have 5 times as much money as her. If Harry gives Jen $18, he will have the same amount of money as her. How much money does each person have respectively?
- Harry?
- Jen?
|
Case 1 |
Case 2 |
|
Harry |
Jen |
Harry |
Jen |
Before |
5 u - 11 |
1 u + 11 |
3 u + 18 |
3 u - 18 |
Change |
+ 11 |
- 11 |
- 18 |
+ 18 |
After |
5 u |
1 u |
3 u |
3 u |
(a)
If Jen gives Harry some money or Harry gives Jen some money, the total amount of money remains the same.
Total amount that Harry and Jen have in the end for both cases
= 5 u + 1 u
= 6 u
Amount that Harry and Jen each has in the end in Case 2
= 6 u ÷ 2
= 3 u
The amount that Harry has at first in Case 1 and Case 2 is the same.
5 u - 11 = 3 u + 18
5 u - 3 u = 18 + 11
1 u = 29
Amount that Harry has
= 3 u + 18
= 3 x 29 + 18
= 87 + 18
= $105
(b)
Amount that Jen has
= 1 u + 11
= 29 + 11
= $40
Answer(s): (a) $105; (b) $40