Question

wilson middle school wants to rent tables for their weeklong art festival. one rental company charges a $20 setup fee and $12 per table for the week. another rental company charges a $30 setup fee and $10 per table for the week. how many tables can the school rent for the charge to be the same for both companies?
let c represent the number of tables. select the correct values to write an equation to represent the situation.
first rental company
select choice + select choice c
=
second rental company
select choice + select choice c

part b
solve the equation. how many tables can the school rent for the charge to be the same for both companies?
____ tables

Explanation:

Step1: Define cost functions

Let \( C_1 \) be cost of First Rental Company: setup fee $20, $12 per table. So \( C_1 = 20 + 12c \).
Let \( C_2 \) be cost of Second Rental Company: setup fee $30, $10 per table. So \( C_2 = 30 + 10c \).

Step2: Set costs equal

To find when charges are same, set \( C_1 = C_2 \):
\( 20 + 12c = 30 + 10c \).

Step3: Solve for \( c \)

Subtract \( 10c \) and 20 from both sides:
\( 12c - 10c = 30 - 20 \)
\( 2c = 10 \).

Divide by 2:
\( c = \frac{10}{2} = 5 \).

Answer:

5