Question

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analia is a school district manager. here are some details about two schools in her district for the last school year:

	school a	school b
number of teachers	100	350
graduation rate	86%	90%
budget per student	$10,500	$10,000
% of students in sports clubs	62%	68%
number of sports medals won	9	7
sat average	1200	1050
sat range (max - min)	900	700

analia wants to know which school has higher academic achievements relative to the number of teachers per student.

1. analia thought of two different ways to define this quantity. identify these two definitions among the following options.

choose 2 answers:
a graduation rate divided by number of teachers
b graduation rate divided by teachers per student
c sat average divided by number of teachers
d sat average divided by teachers per student

1. determine which school has higher academic achievements relative to the number of teachers per student, according to the two definitions. did you get the same result for both definitions?

Explanation:

Part 1: Identifying the two definitions

To determine academic achievements relative to teachers per student, we need to relate an academic metric (graduation rate or SAT average) to the teachers per student ratio. Teachers per student is calculated as (number of students / number of teachers). So, the two valid definitions should be an academic metric divided by teachers per student. Option B uses graduation rate (academic) divided by teachers per student, and Option D uses SAT average (academic) divided by teachers per student. Options A and C divide by number of teachers (not teachers per student), so they are incorrect.

For both definitions (graduation rate / teachers per student and SAT average / teachers per student), School B has a higher value. So the result is the same for both definitions.

Answer:

B. Graduation rate divided by teachers per student
D. SAT average divided by teachers per student

Part 2: Calculating for each school and comparing

First, calculate teachers per student for each school:

• School A: Teachers per student = $\frac{\text{Number of students}}{\text{Number of teachers}} = \frac{3000}{100} = 30$
• School B: Teachers per student = $\frac{4000}{350} \approx 11.43$

Definition 1: Graduation rate divided by teachers per student

• School A: $\frac{86\%}{30} = \frac{0.86}{30} \approx 0.0287$
• School B: $\frac{90\%}{11.43} = \frac{0.90}{11.43} \approx 0.0787$

Here, School B has a higher value.

Definition 2: SAT average divided by teachers per student

• School A: $\frac{1200}{30} = 40$
• School B: $\frac{1050}{11.43} \approx 91.86$

Here, School B has a higher value.