Fred and Joelle has some money each. If Joelle gives Fred $11, he will have 3 times as much money as her. If Fred gives Joelle $17, he will have the same amount of money as her. How much money does each person have respectively?
- Fred?
- Joelle?
| |
Case 1 |
Case 2 |
| |
Fred |
Joelle |
Fred |
Joelle |
| Before |
3 u - 11 |
1 u + 11 |
2 u + 17 |
2 u - 17 |
| Change |
+ 11 |
- 11 |
- 17 |
+ 17 |
| After |
3 u |
1 u |
2 u |
2 u |
(a)
If Joelle gives Fred some money or Fred gives Joelle some money, the total amount of money remains the same.
Total amount that Fred and Joelle have in the end for both cases
= 3 u + 1 u
= 4 u
Amount that Fred and Joelle each has in the end in Case 2
= 4 u ÷ 2
= 2 u
The amount that Fred has at first in Case 1 and Case 2 is the same.
3 u - 11 = 2 u + 17
3 u - 2 u = 17 + 11
1 u = 28
Amount that Fred has
= 2 u + 17
= 2 x 28 + 17
= 56 + 17
= $73
(b)
Amount that Joelle has
= 1 u + 11
= 28 + 11
= $39
Answer(s): (a) $73; (b) $39
