Math Problem Statement

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 students [3000] [4000] Number of teachers [190] [380] Graduation rate [86%] [90%] Budget per student [$10{,}500] [$10{,}000] % of students in sports club [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: Choose 2 answers: (Choice A) Graduation rate divided by number of teachers A Graduation rate divided by number of teachers (Choice B) Graduation rate divided by teachers per student B Graduation rate divided by teachers per student (Choice C) SAT average divided by number of teachers C SAT average divided by number of teachers (Choice D) SAT average divided by teachers per student D SAT average divided by teachers per student
  2. 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? Choose 1 answer: Choose 1 answer: (Choice A) Yes. According to both definitions, school A has higher academic achievements relative to the number of teachers per student. A Yes. According to both definitions, school A has higher academic achievements relative to the number of teachers per student. (Choice B) Yes. According to both definitions, school B has higher academic achievements relative to the number of teachers per student. B Yes. According to both definitions, school B has higher academic achievements relative to the number of teachers per student. (Choice C) No. The definitions have opposite results. C No. The definitions have opposite results.

Solution

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Math Problem Analysis

Mathematical Concepts

Ratios
Proportions
Division
SAT scores
Graduation rates

Formulas

Teachers per student = Number of teachers / Number of students
Graduation rate per teacher = Graduation rate / Number of teachers
SAT per teacher-student ratio = SAT average / Teachers per student

Theorems

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Suitable Grade Level

Grades 8-10