Metropolitan Middle School has 564 students and 24 teachers. Eastern Middle School has 623 students and 28 teachers. Which school has the lower unit rate of students per teacher?

Question

Noah Archer · Accepted Answer

Eastern Middle School

The final desired answer has the form of ratios – students/teacher. We set up the same ratio for each class, and then compare the two values. #(564/24) and (623/28)# We can solve this numerically for a decimal answer, or “cross multiply” by the denominators to get equivalent values of students per teacher. Direct method: 564/24 = 22.56 students/teacher 623/28 = 22.25 students/teacher Fractional method: #(564/24) * (28/28) = (15792/672)# and #(623/28) * (24/24) = (14952/672)# In each case we obtain the same conclusion that the Eastern Middle School has a very slight lower unit rate.

Cameron Arnold · Answer

undefined To find the unit rate of students per teacher for each school, divide the number of students by the number of teachers for each school.

For Metropolitan Middle School:
Unit rate = Number of students / Number of teachers
Unit rate = 564 students / 24 teachers
Unit rate ≈ 23.5 students per teacher

For Eastern Middle School:
Unit rate = Number of students / Number of teachers
Unit rate = 623 students / 28 teachers
Unit rate ≈ 22.25 students per teacher

Comparing the unit rates, we see that Eastern Middle School has the lower unit rate of students per teacher, with approximately 22.25 students per teacher, compared to Metropolitan Middle School's approximately 23.5 students per teacher.