Jack and Nora has some money each. If Nora gives Jack $17, he will have 7 times as much money as her. If Jack gives Nora $16, he will have the same amount of money as her. How much money does each person have respectively?
- Jack?
- Nora?
| |
Case 1 |
Case 2 |
| |
Jack |
Nora |
Jack |
Nora |
| Before |
7 u - 17 |
1 u + 17 |
4 u + 16 |
4 u - 16 |
| Change |
+ 17 |
- 17 |
- 16 |
+ 16 |
| After |
7 u |
1 u |
4 u |
4 u |
(a)
If Nora gives Jack some money or Jack gives Nora some money, the total amount of money remains the same.
Total amount that Jack and Nora have in the end for both cases
= 7 u + 1 u
= 8 u
Amount that Jack and Nora each has in the end in Case 2
= 8 u ÷ 2
= 4 u
The amount that Jack has at first in Case 1 and Case 2 is the same.
7 u - 17 = 4 u + 16
7 u - 4 u = 16 + 17
1 u = 33
Amount that Jack has
= 4 u + 16
= 4 x 33 + 16
= 132 + 16
= $148
(b)
Amount that Nora has
= 1 u + 17
= 33 + 17
= $50
Answer(s): (a) $148; (b) $50
