Question

school a school b
number of students number number
number of teachers number number
graduation rate rate rate
budget per student $15,000 $10,000
% of students in sports club rate rate
number of sports medals won 9 7
sat average 1200 1050
sat range (max - min) 800 700
analla wants to know which school has higher athletic achievements relative to the budget per student.

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

choose 2 answers:
a number of sports medals won divided by budget per student.
b number of sports medals won divided by teachers per student.
c % of students in sports club divided by budget per student.
d % of students in sports club divided by graduation rate.

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

choose 1 answer:

• yes. according to both definitions, school a has higher athletic achievements relative to the budget per student.
• yes. according to both definitions, school b has higher athletic achievements relative to the budget per student.
• no. the definitions have opposite results.

Explanation:

1)

To determine athletic achievements relative to budget per student, we need ratios involving athletic - related metrics (number of sports medals won, % of students in sports club) and budget per student. Option A uses number of sports medals won (athletic achievement) divided by budget per student. Option C uses % of students in sports club (athletic - related participation) divided by budget per student. Options B and D do not involve budget per student, so they are not relevant.

Step 1: Calculate for Definition A (Number of sports medals won / Budget per student)

• For School A: Number of sports medals won = 9, Budget per student = $15,000. So the ratio is $\frac{9}{15000}= 6\times10^{-4}$
• For School B: Number of sports medals won = 7, Budget per student = $10,000. So the ratio is $\frac{7}{10000}=7\times 10^{-4}$

Step 2: Calculate for Definition C (% of students in sports club / Budget per student)

• For School A: % of students in sports club = 80% = 0.8, Budget per student = $15,000. So the ratio is $\frac{0.8}{15000}\approx5.33\times 10^{-5}$
• For School B: % of students in sports club = 60% = 0.6, Budget per student = $10,000. So the ratio is $\frac{0.6}{10000}=6\times 10^{-5}$

Step 3: Compare the results

For Definition A, School B has a higher ratio ($7\times 10^{-4}>6\times 10^{-4}$). For Definition C, School B has a higher ratio ($6\times 10^{-5}>5.33\times 10^{-5}$). Wait, no, wait, let's recalculate Definition A:

Wait, School A: 9 medals, $15,000 budget. $\frac{9}{15000}=0.0006$

School B: 7 medals, $10,000 budget. $\frac{7}{10000} = 0.0007$. So School B is higher for A.

Definition C: School A: 80% = 0.8, $15,000. $\frac{0.8}{15000}\approx0.0000533$

School B: 60% = 0.6, $10,000. $\frac{0.6}{10000}=0.00006$. So School B is higher for C? Wait, no, maybe I made a mistake. Wait, the question is about "athletic achievements relative to budget per student". Wait, maybe the initial calculation is wrong. Wait, let's re - express:

For Definition A:

School A: $\frac{9}{15000}= 0.0006$ medals per dollar

School B: $\frac{7}{10000}=0.0007$ medals per dollar. So School B is better for A.

For Definition C:

School A: $\frac{0.8}{15000}\approx5.33\times 10^{-5}$ (students in sports club per dollar)

School B: $\frac{0.6}{10000}=6\times 10^{-5}$ (students in sports club per dollar). So School B is better for C? But that's not the case. Wait, maybe I mixed up the ratio. Wait, maybe it's (budget per student)/ (athletic metric)? No, the question says "athletic achievements relative to budget per student", so it's (athletic metric)/ (budget per student).

Wait, but let's check the numbers again. School A: budget per student is $15,000, School B: $10,000. Number of medals: A has 9, B has 7. % in sports club: A has 80%, B has 60%.

For Definition A (medals / budget):

A: 9 / 15000 = 0.0006

B: 7 / 10000 = 0.0007. So B is higher.

For Definition C (% in sports club / budget):

A: 0.8 / 15000 ≈ 0.0000533

B: 0.6 / 10000 = 0.00006. So B is higher. But that would mean the answer is "Yes. According to both definitions, School B has higher athletic achievements relative to the budget per student." But wait, maybe I made a mistake in the ratio direction. Wait, maybe it's (budget per student)/(athletic metric), which would be the cost per athletic achievement. Let's try that:

For Definition A (budget per student / number of medals):

A: 15000 / 9 ≈ 1666.67

B: 10000 / 7 ≈ 1428.57. So B has a lower cost per medal, meaning higher achievement relative to budget.

For Definition C (budget per student / % in sports club):

A: 15000 / 0.8 = 18750

B: 10000 / 0.6 ≈ 16666.67. So B has a lower cost per % of students in sports club, meaning higher achievement relative to budget.

So in both cases, School B is better. But wait, the options:

Option 1: Yes. According to both definitions, School A has higher athletic achievements relative to the budget per student.

Option 2: Yes. According to both definitions, School B has higher athletic achievements relative to the budget per student.

Option 3: No. The definitions ha…

Answer:

A. Number of sports medals won divided by budget per student, C. % of students in sports club divided by budget per student

2)