Bryan and Marion has some money each. If Marion gives Bryan $11, he will have 3 times as much money as her. If Bryan gives Marion $14, he will have the same amount of money as her. How much money does each person have respectively?
- Bryan?
- Marion?
| |
Case 1 |
Case 2 |
| |
Bryan |
Marion |
Bryan |
Marion |
| Before |
3 u - 11 |
1 u + 11 |
2 u + 14 |
2 u - 14 |
| Change |
+ 11 |
- 11 |
- 14 |
+ 14 |
| After |
3 u |
1 u |
2 u |
2 u |
(a)
If Marion gives Bryan some money or Bryan gives Marion some money, the total amount of money remains the same.
Total amount that Bryan and Marion have in the end for both cases
= 3 u + 1 u
= 4 u
Amount that Bryan and Marion each has in the end in Case 2
= 4 u ÷ 2
= 2 u
The amount that Bryan has at first in Case 1 and Case 2 is the same.
3 u - 11 = 2 u + 14
3 u - 2 u = 14 + 11
1 u = 25
Amount that Bryan has
= 2 u + 14
= 2 x 25 + 14
= 50 + 14
= $64
(b)
Amount that Marion has
= 1 u + 11
= 25 + 11
= $36
Answer(s): (a) $64; (b) $36
