Water Wizards and Pat's Pipes are two companies that offer plumbing and heating services. Both charge a base fee for all service appointments and an hourly labor rate for repairs. The two companies charge the same base fee, but Water Wizards charges a higher hourly rate than Pat's Pipes. If the total amount Water Wizards charges for $x$ hours of repairs is modeled by the expression $45 x+60$ , which expression could represent the total amount Pat's Pipes would charge for the same amount of time spent on repairs? $\newline$ A. $55 x+60$ $\newline$ B. $45 x+50$ $\newline$ C. $35 x+60$ $\newline$ D. $45 x+70$

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Q. Water Wizards and Pat's Pipes are two companies that offer plumbing and heating services. Both charge a base fee for all service appointments and an hourly labor rate for repairs. The two companies charge the same base fee, but Water Wizards charges a higher hourly rate than Pat's Pipes. If the total amount Water Wizards charges for

x

hours of repairs is modeled by the expression

45 x+60

, which expression could represent the total amount Pat's Pipes would charge for the same amount of time spent on repairs?

\newline

55 x+60

\newline

45 x+50

\newline

35 x+60

\newline

45 x+70

Analyze Information: Let's analyze the given information: $\newline$ - Both companies charge the same base fee. $\newline$ - Water Wizards charges a higher hourly rate than Pat's Pipes. $\newline$ - The total charge by Water Wizards for $x$ hours of repairs is given by the expression $45x + 60$ . $\newline$ We need to find an expression that represents Pat's Pipes' total charge for $x$ hours of repairs, which should have the same base fee but a lower hourly rate.
Eliminate Options: Since both companies charge the same base fee, we can rule out any options that have a different base fee from Water Wizards. Water Wizards' base fee is represented by the constant term in the expression, which is $60$ . Looking at the options, we can eliminate any that do not have a base fee of $60$ . Option A: $55x + 60$ (Base fee is $60$ , but hourly rate is lower than Water Wizards, which is not possible since Water Wizards has the higher hourly rate.) Option B: $45x + 50$ (Base fee is $50$ , which is different from Water Wizards' base fee of $60$ .) Option C: $35x + 60$ (Base fee is $60$ , and hourly rate is lower than Water Wizards.) Option D: $45x + 70$ (Base fee is $60$ $0$ , which is different from Water Wizards' base fee of $60$ .) We can eliminate options B and D because the base fees are not the same as Water Wizards'.
Compare Hourly Rates: Now we need to compare the hourly rates. Water Wizards charges an hourly rate of $45$ (as seen in the expression $45x$ ). We are looking for an expression where Pat's Pipes charges a lower hourly rate. $\newline$ Option A: $55x + 60$ (Hourly rate is $55$ , which is higher than Water Wizards' rate of $45$ , so this is not possible.) $\newline$ Option C: $35x + 60$ (Hourly rate is $35$ , which is lower than Water Wizards' rate of $45$ .) $\newline$ Since Pat's Pipes charges a lower hourly rate than Water Wizards, option C is the correct expression that represents the total amount Pat's Pipes would charge for $x$ hours of repairs.