Final answer:
The math teacher will take 108 minutes to grade all 36 final exams, calculated by setting up a proportion based on the given rate of grading 10 exams in 30 minutes.
Step-by-step explanation:
To calculate how many minutes it will take the math teacher to grade all 36 exams, we need to set up a proportion based on the rate provided. The teacher can grade 10 exams in 30 minutes, so the proportion will compare the number of exams graded to the time it takes:
- 10 exams / 30 minutes = 36 exams / x minutes
We can now solve for x, which represents the total time to grade 36 exams:
- 10/x = 36/30
- x = (36 exams * 30 minutes) / 10 exams
- x = 1080 / 10
- x = 108 minutes
Therefore, it will take the math teacher 108 minutes to grade all 36 final exams.