Jack and Fiona has some money each. If Fiona gives Jack $16, he will have 7 times as much money as her. If Jack gives Fiona $17, he will have the same amount of money as her. How much money does each person have respectively?
- Jack?
- Fiona?
|
Case 1 |
Case 2 |
|
Jack |
Fiona |
Jack |
Fiona |
Before |
7 u - 16 |
1 u + 16 |
4 u + 17 |
4 u - 17 |
Change |
+ 16 |
- 16 |
- 17 |
+ 17 |
After |
7 u |
1 u |
4 u |
4 u |
(a)
If Fiona gives Jack some money or Jack gives Fiona some money, the total amount of money remains the same.
Total amount that Jack and Fiona have in the end for both cases
= 7 u + 1 u
= 8 u
Amount that Jack and Fiona 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 - 16 = 4 u + 17
7 u - 4 u = 17 + 16
1 u = 33
Amount that Jack has
= 4 u + 17
= 4 x 33 + 17
= 132 + 17
= $149
(b)
Amount that Fiona has
= 1 u + 16
= 33 + 16
= $49
Answer(s): (a) $149; (b) $49