Question

1. the cafeteria tables at jackson middle school can hold 12 students each. if there are 50 cafeteria tables, which equation can be used to find (c) the seating capacity of the cafeteria?

a. c + 12 = 50
b. 12c = 50
c. \\(\frac{c}{12} = 50\\)
d. \\(\frac{50}{c} = 12\\)
50×12 = c

Explanation:

Step1: Understand the problem

We need to find the equation for the total seating capacity \( c \). Each table holds 12 students, and there are 50 tables. So total capacity \( c \) should be the number of tables times students per table, i.e., \( c = 12\times50 \). Now let's analyze each option:

Step2: Analyze Option a

Equation: \( c + 12 = 50 \). This would imply \( c=50 - 12 \), which is not related to total capacity (adding students per table and tables doesn't make sense). So a is wrong.

Step3: Analyze Option b

Equation: \( 12c = 50 \). This would imply \( c=\frac{50}{12} \), which is not the total capacity (multiplying students per table and total capacity to get tables is wrong). So b is wrong.

Step4: Analyze Option c

Equation: \( \frac{c}{12}=50 \). If we solve for \( c \), we get \( c = 12\times50 \), which matches the total capacity (total capacity divided by students per table gives number of tables). So this equation is correct.

Step5: Analyze Option d

Equation: \( \frac{50}{c}=12 \). Solving for \( c \) gives \( c=\frac{50}{12} \), which is not the total capacity (tables divided by total capacity gives students per table, which is not 12 here). So d is wrong.

Answer:

c. \(\frac{c}{12} = 50\)