SAT Math Problem (2)

Question

C₁ = 640 + 12mh

 

C₂ = 400 + 15mh 

 

Mrs. Jamerson is having all the rooms on the first floor of her house painted. She has received the two quotes show above where C₁(h) represents the total cost for having the job completed with Company 1, C₂(h)  represents the total cost for having the job done with Company 2, m represents the number of men on the job, and h is the estimated number if hours to complete the job.

 

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If it is determined by both companies (C₁ and C₂) that ten men are necessary to complete the job, what is the least integer number of hours, h, where the total cost to have the house painted by Company 1 would be less than the total cost to have the house painted by Company 2?

Answer 1

Since they both need 10 men, the functions can be changed to C1=640+120h and C2=400+150h.

Since you want C1 to be less than C2, you can set up the inequality below:

640+120h < 400 + 150h

-30 h < -240

     h > 8     You must reverse an inequality when you divide by a negative.

 

So the least integer that satisfies this inequality is h=9.

 

Hope this helped,