Question

Jose is comparing the prices of two carpet cleaning companies. Company A charges $0.40 per square foot of carpet area and an additional $22 per day for services. Company B charges 0.60 per square foot of carpet area and an additional $18 per day for services. Part A: Write equations to represent Company A and Company B's total charges for cleaning a certain carpet area in a day. Define the variable used in the equations. (4 points) Part B: Which company would charge less for cleaning 500 square feet of carpet area? Justify your answer. (3 points) Part C: How much money is saved by using the services of Company A instead of Company B for cleaning 200 square feet of carpet area? (3 points)

Answer 1

Part A: Write equations to represent Company A and Company B's total charges for cleaning to certain carpet area in a day. Define the variable used in the equations. (4 points)
First we define the variables:
x = square foot of carpet area
y = price in $
We now write the equations for each company:
Company A:
y = 0.40x + 22
Company B:
y = 0.60x + 18
Answer:
Company A:
y = 0.40x + 22
Company B:
y = 0.60x + 18

Part B: Which company would charge less for cleaning? 500 square feet of carpet area? Justify your answer. (3 points)
We use the contracted equations in part A and substitute x = 500
We have then:
Company A:
y = 0.40 * (500) +22
y = 222 $
Company B:
y = 0.60x + 18
y = 0.60 * (500) +18
y = $ 318
Answer:
company A would charge less for cleaning 500 square feet of carpet area

Part C: How much money is saved by using the services of Company A instead of Company B for cleaning 200 square feet of carpet area? (3 points)
Company A:
y = 0.40 * (200) +22
y = $ 102
Company B:
y = 0.60x + 18
y = 0.60 * (200) +18
y = $ 138
Then,
138-102 = 36 $
Answer:
is saved about 36 $ by using the services of Company A instead of Company B for cleaning 200 square feet of carpet area