Reggie and Fiona has some money each. If Fiona gives Reggie $13, he will have 3 times as much money as her. If Reggie gives Fiona $17, he will have the same amount of money as her. How much money does each person have respectively?
- Reggie?
- Fiona?
|
Case 1 |
Case 2 |
|
Reggie |
Fiona |
Reggie |
Fiona |
Before |
3 u - 13 |
1 u + 13 |
2 u + 17 |
2 u - 17 |
Change |
+ 13 |
- 13 |
- 17 |
+ 17 |
After |
3 u |
1 u |
2 u |
2 u |
(a)
If Fiona gives Reggie some money or Reggie gives Fiona some money, the total amount of money remains the same.
Total amount that Reggie and Fiona have in the end for both cases
= 3 u + 1 u
= 4 u
Amount that Reggie and Fiona each has in the end in Case 2
= 4 u ÷ 2
= 2 u
The amount that Reggie has at first in Case 1 and Case 2 is the same.
3 u - 13 = 2 u + 17
3 u - 2 u = 17 + 13
1 u = 30
Amount that Reggie has
= 2 u + 17
= 2 x 30 + 17
= 60 + 17
= $77
(b)
Amount that Fiona has
= 1 u + 13
= 30 + 13
= $43
Answer(s): (a) $77; (b) $43