An auto mechanic charges $50 to diagnose a problem and $25 per hour to repair the problem. If [tex]$x$[/tex] represents the total number of hours worked and [tex]$y$[/tex] represents the total charges, which equation represents this situation?
[tex]y=25 x+50[/tex]
[tex]y=50 x+25[/tex]
[tex]y=50 x-25[/tex]
[tex]y=25 x-50[/tex]
Answer (2)
The mechanic charges a fixed fee of $50 for diagnosis.
The mechanic charges $25 per hour for repair, so the repair cost is 25 x .
The total charge y is the sum of the diagnosis fee and the repair cost: y = 25 x + 50 .
The equation representing the situation is y = 25 x + 50 .
Explanation
Problem Analysis Let's analyze the problem. We are given that an auto mechanic charges a fixed fee of $50 to diagnose a problem and an hourly rate of $25 to repair the problem. We need to find an equation that represents the total charges, denoted by y , in terms of the number of hours worked, denoted by x .
Identifying Components of Total Charges The total charges y consist of two parts: the fixed diagnosis fee and the variable repair charges. The diagnosis fee is a constant $50, regardless of the number of hours worked. The repair charges are calculated by multiplying the hourly rate of $25 by the number of hours worked, which is x . So, the repair charges are 25 x .
Formulating the Equation To find the total charges y , we add the diagnosis fee and the repair charges: y = 25 x + 50 . Now, we compare this equation with the given options to find the correct one.
Final Equation The equation that represents the situation is y = 25 x + 50 .
Examples
Imagine you need to hire an electrician to fix a wiring issue in your home. The electrician charges a flat fee for the initial visit and an hourly rate for the repair work. Understanding how to calculate the total cost using a linear equation like the one in this problem helps you budget effectively and compare quotes from different service providers. This same principle applies to various scenarios, such as plumbing services, tutoring fees, or even calculating the cost of a taxi ride, where there's often a base fare plus a per-mile charge. By recognizing and applying this linear equation model, you can make informed decisions about service costs and manage your expenses wisely.
The equation that represents the total charges for the mechanic's services is y = 25 x + 50 , where x is the number of hours worked. This equation includes a $50 diagnosis fee and a $25 per hour repair charge.
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