Bryan and Zara has some money each. If Zara gives Bryan $14, he will have 7 times as much money as her. If Bryan gives Zara $15, he will have the same amount of money as her. How much money does each person have respectively?
- Bryan?
- Zara?
| |
Case 1 |
Case 2 |
| |
Bryan |
Zara |
Bryan |
Zara |
| Before |
7 u - 14 |
1 u + 14 |
4 u + 15 |
4 u - 15 |
| Change |
+ 14 |
- 14 |
- 15 |
+ 15 |
| After |
7 u |
1 u |
4 u |
4 u |
(a)
If Zara gives Bryan some money or Bryan gives Zara some money, the total amount of money remains the same.
Total amount that Bryan and Zara have in the end for both cases
= 7 u + 1 u
= 8 u
Amount that Bryan and Zara each has in the end in Case 2
= 8 u ÷ 2
= 4 u
The amount that Bryan has at first in Case 1 and Case 2 is the same.
7 u - 14 = 4 u + 15
7 u - 4 u = 15 + 14
1 u = 29
Amount that Bryan has
= 4 u + 15
= 4 x 29 + 15
= 116 + 15
= $131
(b)
Amount that Zara has
= 1 u + 14
= 29 + 14
= $43
Answer(s): (a) $131; (b) $43
