Julian and Sarah has some money each. If Sarah gives Julian $11, he will have 7 times as much money as her. If Julian gives Sarah $12, he will have the same amount of money as her. How much money does each person have respectively?
- Julian?
- Sarah?
|
Case 1 |
Case 2 |
|
Julian |
Sarah |
Julian |
Sarah |
Before |
7 u - 11 |
1 u + 11 |
4 u + 12 |
4 u - 12 |
Change |
+ 11 |
- 11 |
- 12 |
+ 12 |
After |
7 u |
1 u |
4 u |
4 u |
(a)
If Sarah gives Julian some money or Julian gives Sarah some money, the total amount of money remains the same.
Total amount that Julian and Sarah have in the end for both cases
= 7 u + 1 u
= 8 u
Amount that Julian and Sarah each has in the end in Case 2
= 8 u ÷ 2
= 4 u
The amount that Julian has at first in Case 1 and Case 2 is the same.
7 u - 11 = 4 u + 12
7 u - 4 u = 12 + 11
1 u = 23
Amount that Julian has
= 4 u + 12
= 4 x 23 + 12
= 92 + 12
= $104
(b)
Amount that Sarah has
= 1 u + 11
= 23 + 11
= $34
Answer(s): (a) $104; (b) $34