Flynn and Zara has some money each. If Zara gives Flynn $12, he will have 3 times as much money as her. If Flynn gives Zara $13, he will have the same amount of money as her. How much money does each person have respectively?
- Flynn?
- Zara?
| |
Case 1 |
Case 2 |
| |
Flynn |
Zara |
Flynn |
Zara |
| Before |
3 u - 12 |
1 u + 12 |
2 u + 13 |
2 u - 13 |
| Change |
+ 12 |
- 12 |
- 13 |
+ 13 |
| After |
3 u |
1 u |
2 u |
2 u |
(a)
If Zara gives Flynn some money or Flynn gives Zara some money, the total amount of money remains the same.
Total amount that Flynn and Zara have in the end for both cases
= 3 u + 1 u
= 4 u
Amount that Flynn and Zara each has in the end in Case 2
= 4 u ÷ 2
= 2 u
The amount that Flynn has at first in Case 1 and Case 2 is the same.
3 u - 12 = 2 u + 13
3 u - 2 u = 13 + 12
1 u = 25
Amount that Flynn has
= 2 u + 13
= 2 x 25 + 13
= 50 + 13
= $63
(b)
Amount that Zara has
= 1 u + 12
= 25 + 12
= $37
Answer(s): (a) $63; (b) $37
