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Sarah needs to find a plumbing company to fix the plumbing in her house. Pat’s Plumbing Company charges a flat rate of $650 to inspect the house plus $25.75 per hour of labor to fix the problem. Her friend Kristin tells her that AAA Plumbing will charge a fee on $675 to inspect the house and an hourly fee of $24.50 for labor. Kristin knows that AAA Plumbing will cost no more than Pat’s Plumbing Company. Which inequality correctly shows the relationship between the total cost of the two plumbing companies?

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Answer:

An inequality correctly shows the relationship between the total cost of the two plumbing companies is [tex]675+24.5x \leq 650+25.75x[/tex]

Step-by-step explanation:

Pat’s Plumbing Company

Cost of inspecting house = $650

Cost of labor per hour = $25.75

Cost of labor in x hours = 25.75x

Total cost = 650+25.75x

AAA Plumbing

Cost of inspecting house = $675

Cost of labor per hour = $24.50

Cost of labor in x hours = 24.5x

Total cost = 675+24.5x

We are given that AAA Plumbing will cost no more than Pat’s Plumbing Company

[tex]675+24.5x \leq 650+25.75x[/tex]

Hence An inequality correctly shows the relationship between the total cost of the two plumbing companies is [tex]675+24.5x \leq 650+25.75x[/tex]

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