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Write a system of equations to describe the situation below, solve using any method, and fill in the blanks.Professor Garrett is grading papers in the teachers' lounge. He has already finished grading assignments, and is grading more assignments per hour. His teaching assistant just came in to help him. He can grade at a rate of 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 Garrett and his assistant will have graded assignments.
Full solution
Q. Write a system of equations to describe the situation below, solve using any method, and fill in the blanks.Professor Garrett is grading papers in the teachers' lounge. He has already finished grading assignments, and is grading more assignments per hour. His teaching assistant just came in to help him. He can grade at a rate of 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 Garrett and his assistant will have graded assignments.
- Define Variables: Let's denote the number of hours Professor Garrett's assistant works as . Since Professor Garrett has already graded assignments and grades more per hour, the total number of assignments he will have graded after hours is .
- Calculate Assignments Graded by Professor Garrett: The assistant grades assignments per hour, so after hours, he will have graded assignments.
- Calculate Assignments Graded by Assistant: For both Professor Garrett and his assistant to have graded the same number of assignments, we set their respective expressions equal to each other:
- Set Up Equation: Now we solve for by subtracting from both sides of the equation:
- Solve for x: Divide both sides by to find the value of x:
- Calculate Total Assignments Graded by Assistant: Now that we know is , we can find out how many assignments they each have graded. Since the assistant has graded assignments per hour, after hours he will have graded: assignments.
- Confirm Total Assignments Graded by Professor Garrett: To confirm that Professor Garrett has graded the same number of assignments, we substitute with in his equation: assignments.
