Answer:
The equation for the situation is:
![5y+2=27](https://tex.z-dn.net/?f=5y%2B2%3D27)
where
represents the number of questions initially assigned to each student by the teacher.
On solving, we find that 5 questions were originally assigned to each student by the teacher.
Step-by-step explanation:
Question:
Five students came for after-school tutoring. Priya’s teacher assigned each of them the same number of problems to complete. Then she assigned 2 more problems to one of the students. 27 problems were assigned in all. Use y as the variable. Write an equation for the situation. Then, find the number of problems originally assigned to each by the teacher.
Given:
Total number of students = 5
Total problems assigned = 27
To find the number of problems originally assigned by the teacher.
Solution:
Let the number of problems originally assigned by the teacher to each student be = ![y](https://tex.z-dn.net/?f=y)
If each student is assigned questions initially.
Then, 5 students was initially assigned = questions
The teacher then assigned 2 more problems to one of the students.
So, the total number of questions now assigned will be given as:
⇒ ![5y+2](https://tex.z-dn.net/?f=5y%2B2)
Total problems assigned = 27
Thus, we have:
![5y+2=27](https://tex.z-dn.net/?f=5y%2B2%3D27)
Solving for
Subtracting both sides by 2.
![5y+2-2=27-2](https://tex.z-dn.net/?f=5y%2B2-2%3D27-2)
![5y=25](https://tex.z-dn.net/?f=5y%3D25)
Dividing both sides by 5.
![\frac{5y}{5}=\frac{25}{5}](https://tex.z-dn.net/?f=%5Cfrac%7B5y%7D%7B5%7D%3D%5Cfrac%7B25%7D%7B5%7D)
∴ ![y=5](https://tex.z-dn.net/?f=y%3D5)
Thus, each student was originally assigned = 5 questions