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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)

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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

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