Jake is comparing the prices of two mattress cleaning companies. company a charges $30 per mattress and an additional $13 as service charges. company b charges $28 per mattress and an additional $15 as service charges. part a: write equations to represent company a's and company b's total mattress cleaning charges for a certain number of mattresses. define the variable used in the equations. (4 points) part b: which company would charge less for cleaning 4 mattresses? justify your answer. (3 points) part c: how much money is saved by using the services of company b instead of company a to clean 7 mattresses? (3 points)

A) A = 30m + 13           B = 28m + 15

B) Company B would charge $6 less for 4 mattresses

C) Company B would charge $12 less for 7 mattresses

Step-by-step explanation:

A. : Write equations to represent Company A's and Company B's total mattress cleaning charges for a certain number of mattresses. Define the variable  used in the equations.

Let's define the variable m to represent the number of mattresses to be cleaned.

For company A, we have a cost per mattress of $30 plus a fixed service fee of $13.  So the equation will be:

A = 30m + 13  

While company B charges $28 per mattress, with a fixed service fee of $15:

B = 28m + 15

That way, we have a good representation of both price structures, using a meaningful variable.

B. Which company would charge less for cleaning 4 mattresses? Justify your answer.

We just have to calculate the cost of cleaning 4 mattresses at both companies:

A = 30m + 13 = 30 (4) + 13 = 120 + 13 = $133

B = 28m + 15 = 28 (4) + 15 = 112 + 15 = $127

Company B would charge $6 less for 4 mattresses

C. How much money is saved by using the services of Company B instead of Company A to clean 7 mattresses?

Again, all we have to do is calculate the cost to clean 7 mattresses at both companies:

A = 30m + 13 = 30 (7) + 13 = 210 + 13 = $223

B = 28m + 15 = 28 (7) + 15 = 196 + 15 = $211

Company B would charge $12 less for 7 mattresses