Do both companies cost the same at 40sq or 35sq or 30q

Question

Two carpet cleaning companies offer the following plans.

clean carpets charges $60 for a house call with an additional $1 per square metre of carpet cleaned.

carpet shine charges $3 per square metre of carpet cleaned with no additional charges.

plot a line to represent the cost of both companies depending on the size of the carpet and interpret the meaning of the point of the two lines.

Answer 1

Let the size of the carpet be S meters^2 and C be cost.

equation for clean carpet ---> C = S + 60

equation for carpet shine ---> C = 3S

Cost of carpet shine increases much more faster than the clean carpet.

cost of carpet shine is less than clean carpet for S < 30.

cost of carpet shine is greater than clean carpet for S > 30.

cost of carpet shine is equal to clean carpet for S = 30.