Jack and Zara has some money each. If Zara gives Jack $17, he will have 5 times as much money as her. If Jack gives Zara $16, he will have the same amount of money as her. How much money does each person have respectively?
- Jack?
- Zara?
| |
Case 1 |
Case 2 |
| |
Jack |
Zara |
Jack |
Zara |
| Before |
5 u - 17 |
1 u + 17 |
3 u + 16 |
3 u - 16 |
| Change |
+ 17 |
- 17 |
- 16 |
+ 16 |
| After |
5 u |
1 u |
3 u |
3 u |
(a)
If Zara gives Jack some money or Jack gives Zara some money, the total amount of money remains the same.
Total amount that Jack and Zara have in the end for both cases
= 5 u + 1 u
= 6 u
Amount that Jack and Zara each has in the end in Case 2
= 6 u ÷ 2
= 3 u
The amount that Jack has at first in Case 1 and Case 2 is the same.
5 u - 17 = 3 u + 16
5 u - 3 u = 16 + 17
1 u = 33
Amount that Jack has
= 3 u + 16
= 3 x 33 + 16
= 99 + 16
= $115
(b)
Amount that Zara has
= 1 u + 17
= 33 + 17
= $50
Answer(s): (a) $115; (b) $50
