To address Analia's inquiry about the SAT range relative to the resources invested per student, we shall look at two different ways to define this relationship. Let’s explore these definitions step by step.
### First Definition:
SAT range divided by budget per student
1. School A:
- SAT range: 900
- Budget per student: 10500
Calculation:
[tex]\[
\text{Quantity 1}_A = \frac{\text{SAT range}_A}{\text{Budget per student}_A} = \frac{900}{10500}
\][/tex]
The result is approximately:
[tex]\[
\text{Quantity 1}_A \approx 0.0857
\][/tex]
2. School B:
- SAT range: 700
- Budget per student: 10000
Calculation:
[tex]\[
\text{Quantity 1}_B = \frac{\text{SAT range}_B}{\text{Budget per student}_B} = \frac{700}{10000}
\][/tex]
The result is:
[tex]\[
\text{Quantity 1}_B = 0.07
\][/tex]
Using this definition, we get:
[tex]\[
0.0857 \quad \text{(School A)} \quad \text{and} \quad 0.07 \quad \text{(School B)}
\][/tex]
### Second Definition:
Budget per student divided by SAT range
1. School A:
- Budget per student: 10500
- SAT range: 900
Calculation:
[tex]\[
\text{Quantity 2}_A = \frac{\text{Budget per student}_A}{\text{SAT range}_A} = \frac{10500}{900}
\][/tex]
The result is approximately:
[tex]\[
\text{Quantity 2}_A \approx 11.67
\][/tex]
2. School B:
- Budget per student: 10000
- SAT range: 700
Calculation:
[tex]\[
\text{Quantity 2}_B = \frac{\text{Budget per student}_B}{\text{SAT range}_B} = \frac{10000}{700}
\][/tex]
The result is approximately:
[tex]\[
\text{Quantity 2}_B \approx 14.29
\][/tex]
Using this definition, we get:
[tex]\[
11.67 \quad \text{(School A)} \quad \text{and} \quad 14.29 \quad \text{(School B)}
\][/tex]
### Conclusion
From the two definitions:
1. SAT range divided by budget per student:
[tex]\[
0.0857 \quad \text{(School A)} \quad \text{vs.} \quad 0.07 \quad \text{(School B)}
\][/tex]
2. Budget per student divided by SAT range:
[tex]\[
11.67 \quad \text{(School A)} \quad \text{vs.} \quad 14.29 \quad \text{(School B)}
\][/tex]
Therefore, these two definitions can be chosen to compare the SAT range relative to the resources invested per student.
