Write a system of equations to describe the situation below, solve using substitution, and in the blanks. Professor Conley is grading papers in the teachers' lounge. He has already finished rading 8 assignments, and is grading 2 more assignments per hourHis teaching assistant just came in to help him. She can grade at a rate of 6 assignments every hour. At some point, they will be finished and will have graded the same number of papers. How long will that take? How many assignments will they each have graded? In hours, both Professor Conley and his assistant will have graded assignments.
Let x be the number of hours it will take for Professor Conley and his assistant to finish grading all the papers.
The number of papers Professor Conley has graded is 8 + 2x
The number of papers his assistant has graded is 6x
Since they will have graded the same number of papers at some point, we can set the two equations equal to each other:
8 + 2x = 6x
Subtracting 2x from both sides:
8 = 4x
Dividing by 4:
x = 2
Therefore, it will take 2 hours for Professor Conley and his assistant to finish grading all the papers.
The number of papers each of them will have graded:
Professor Conley: 8 + 2(2) = 12 papers
Assistant: 6(2) = 12 papers
Therefore, both Professor Conley and his assistant will have graded 12 assignments each in 2 hours.