Bryan and Anna has some money each. If Anna gives Bryan $11, he will have 3 times as much money as her. If Bryan gives Anna $15, he will have the same amount of money as her. How much money does each person have respectively?
- Bryan?
- Anna?
| |
Case 1 |
Case 2 |
| |
Bryan |
Anna |
Bryan |
Anna |
| Before |
3 u - 11 |
1 u + 11 |
2 u + 15 |
2 u - 15 |
| Change |
+ 11 |
- 11 |
- 15 |
+ 15 |
| After |
3 u |
1 u |
2 u |
2 u |
(a)
If Anna gives Bryan some money or Bryan gives Anna some money, the total amount of money remains the same.
Total amount that Bryan and Anna have in the end for both cases
= 3 u + 1 u
= 4 u
Amount that Bryan and Anna 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 + 15
3 u - 2 u = 15 + 11
1 u = 26
Amount that Bryan has
= 2 u + 15
= 2 x 26 + 15
= 52 + 15
= $67
(b)
Amount that Anna has
= 1 u + 11
= 26 + 11
= $37
Answer(s): (a) $67; (b) $37
