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? A. 55 x+60 B. 45 x+50 C. 35 x+60 D. 45 x+70

Question

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? A.  55 x+60 B.  45 x+50 C.  35 x+60 D.  45 x+70

Bytelearn · Accepted Answer

Analyze Information: Let's analyze the given information: - Both companies charge the same base fee. - Water Wizards charges a higher hourly rate than Pat's Pipes. - The total charge by Water Wizards for x hours of repairs is given by the expression 45x + 60. 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 70, 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. Option A: 55x + 60 (Hourly rate is 55, which is higher than Water Wizards' rate of 45, so this is not possible.) Option C: 35x + 60 (Hourly rate is 35, which is lower than Water Wizards' rate of 45.) 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.

Full solution

More problems from Interpret parts of quadratic expressions: word problems

Related topics