Fabian and Lynn has some money each. If Lynn gives Fabian $17, he will have 3 times as much money as her. If Fabian gives Lynn $14, he will have the same amount of money as her. How much money does each person have respectively?
- Fabian?
- Lynn?
| |
Case 1 |
Case 2 |
| |
Fabian |
Lynn |
Fabian |
Lynn |
| Before |
3 u - 17 |
1 u + 17 |
2 u + 14 |
2 u - 14 |
| Change |
+ 17 |
- 17 |
- 14 |
+ 14 |
| After |
3 u |
1 u |
2 u |
2 u |
(a)
If Lynn gives Fabian some money or Fabian gives Lynn some money, the total amount of money remains the same.
Total amount that Fabian and Lynn have in the end for both cases
= 3 u + 1 u
= 4 u
Amount that Fabian and Lynn each has in the end in Case 2
= 4 u ÷ 2
= 2 u
The amount that Fabian has at first in Case 1 and Case 2 is the same.
3 u - 17 = 2 u + 14
3 u - 2 u = 14 + 17
1 u = 31
Amount that Fabian has
= 2 u + 14
= 2 x 31 + 14
= 62 + 14
= $76
(b)
Amount that Lynn has
= 1 u + 17
= 31 + 17
= $48
Answer(s): (a) $76; (b) $48
