Question

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)

Answer 1

[Part A]
company A -> A=30m+13
company B -> B=28m+15

A=company A
B=company B
m= number of mattresses

[Part B]
Price charged to clean 4 mattresses
company A= $133
company B= $127

Justification
A=30(4)+13 B=28(4)+15
A=120+13 B=112+15
A=133 B=127

Company B would charge less. Even though the y-intercept is higher, the slope has a lower value which makes company A grow at a faster rate.

[Part C]
If you use company B instead of company A to clean 7 mattresses you will save 12 dollars. The price to clean 7 mattresses with company A is 223 while company B costs 211.

Company A: A=30(7)+13=223
Company B: B=28(7)+15=211