Flynn and Sabrina has some money each. If Sabrina gives Flynn $17, he will have 5 times as much money as her. If Flynn gives Sabrina $14, he will have the same amount of money as her. How much money does each person have respectively?
- Flynn?
- Sabrina?
| |
Case 1 |
Case 2 |
| |
Flynn |
Sabrina |
Flynn |
Sabrina |
| Before |
5 u - 17 |
1 u + 17 |
3 u + 14 |
3 u - 14 |
| Change |
+ 17 |
- 17 |
- 14 |
+ 14 |
| After |
5 u |
1 u |
3 u |
3 u |
(a)
If Sabrina gives Flynn some money or Flynn gives Sabrina some money, the total amount of money remains the same.
Total amount that Flynn and Sabrina have in the end for both cases
= 5 u + 1 u
= 6 u
Amount that Flynn and Sabrina each has in the end in Case 2
= 6 u ÷ 2
= 3 u
The amount that Flynn has at first in Case 1 and Case 2 is the same.
5 u - 17 = 3 u + 14
5 u - 3 u = 14 + 17
1 u = 31
Amount that Flynn has
= 3 u + 14
= 3 x 31 + 14
= 93 + 14
= $107
(b)
Amount that Sabrina has
= 1 u + 17
= 31 + 17
= $48
Answer(s): (a) $107; (b) $48
