Will and Penelope has some money each. If Penelope gives Will $11, he will have 3 times as much money as her. If Will gives Penelope $19, he will have the same amount of money as her. How much money does each person have respectively?
- Will?
- Penelope?
|
Case 1 |
Case 2 |
|
Will |
Penelope |
Will |
Penelope |
Before |
3 u - 11 |
1 u + 11 |
2 u + 19 |
2 u - 19 |
Change |
+ 11 |
- 11 |
- 19 |
+ 19 |
After |
3 u |
1 u |
2 u |
2 u |
(a)
If Penelope gives Will some money or Will gives Penelope some money, the total amount of money remains the same.
Total amount that Will and Penelope have in the end for both cases
= 3 u + 1 u
= 4 u
Amount that Will and Penelope each has in the end in Case 2
= 4 u ÷ 2
= 2 u
The amount that Will has at first in Case 1 and Case 2 is the same.
3 u - 11 = 2 u + 19
3 u - 2 u = 19 + 11
1 u = 30
Amount that Will has
= 2 u + 19
= 2 x 30 + 19
= 60 + 19
= $79
(b)
Amount that Penelope has
= 1 u + 11
= 30 + 11
= $41
Answer(s): (a) $79; (b) $41