Owen and Sarah has some money each. If Sarah gives Owen $14, he will have 7 times as much money as her. If Owen gives Sarah $12, he will have the same amount of money as her. How much money does each person have respectively?
- Owen?
- Sarah?
|
Case 1 |
Case 2 |
|
Owen |
Sarah |
Owen |
Sarah |
Before |
7 u - 14 |
1 u + 14 |
4 u + 12 |
4 u - 12 |
Change |
+ 14 |
- 14 |
- 12 |
+ 12 |
After |
7 u |
1 u |
4 u |
4 u |
(a)
If Sarah gives Owen some money or Owen gives Sarah some money, the total amount of money remains the same.
Total amount that Owen and Sarah have in the end for both cases
= 7 u + 1 u
= 8 u
Amount that Owen and Sarah each has in the end in Case 2
= 8 u ÷ 2
= 4 u
The amount that Owen has at first in Case 1 and Case 2 is the same.
7 u - 14 = 4 u + 12
7 u - 4 u = 12 + 14
1 u = 26
Amount that Owen has
= 4 u + 12
= 4 x 26 + 12
= 104 + 12
= $116
(b)
Amount that Sarah has
= 1 u + 14
= 26 + 14
= $40
Answer(s): (a) $116; (b) $40