Question

3 in a survey, 13 out of 20 teachers respond yes to a proposal for a new after-school club. in the same survey, 37 out of 50 students respond yes.
a. which group is more in favor of the new after-school club, teachers or students? show your work.
b. check your answer to problem 3a. show your work.

Explanation:

Step1: Calculate teacher approval rate

$\frac{13}{20} = 0.65$ or $65\%$

Step2: Calculate student approval rate

$\frac{37}{50} = 0.74$ or $74\%$

Step3: Compare the two rates

$74\% > 65\%$

Step4: Verify via common denominator

$\frac{13}{20} = \frac{13 \times 5}{20 \times 5} = \frac{65}{100}$
$\frac{37}{50} = \frac{37 \times 2}{50 \times 2} = \frac{74}{100}$
$\frac{74}{100} > \frac{65}{100}$

Answer:

a. The students are more in favor of the new after-school club.
b. The verification confirms that $\frac{74}{100}$ (student approval) is greater than $\frac{65}{100}$ (teacher approval), so the answer from part a is correct.