Question

a car mechanic charges an initial fee to inspect a car plus an hourly rate to repair the car if no new parts are needed. one day the mechanic spent 3 hours working on a car and charged $130. after working on the car for 8 hours the mechanic charged $305. what is the rate the mechanic charges per hour? a. $20 b. $35 c. $55 d. $85 question 5.b write an equation that could represent the total amount charged, y, after x hours of work. y = (select) x + (select)

Explanation:

Step1: Set up equation for first - case

Let the initial fee be $a$ and the hourly rate be $r$. For the first case where $x = 3$ hours and $y=130$, we have the equation $y=a + rx$, so $130=a + 3r$.

Step2: Set up equation for second - case

For the second case where $x = 8$ hours and $y = 305$, we have the equation $305=a+8r$.

Step3: Solve the system of equations

Subtract the first equation from the second equation: $(a + 8r)-(a + 3r)=305 - 130$.
Simplify the left - hand side: $a+8r - a - 3r=5r$, and the right - hand side is $175$. So $5r=175$.

Step4: Find the hourly rate

Solve for $r$: $r=\frac{175}{5}=35$.

To find the equation for the total amount charged $y$ after $x$ hours, we use the slope - intercept form $y=a+rx$. We know $r = 35$. Substitute $r = 35$ into the first equation $130=a + 3\times35$, then $130=a+105$, and $a=130 - 105 = 25$. So the equation is $y = 25+35x$.

Answer:

The rate per hour is $\$35$, and the equation is $y=25 + 35x$. The multiple - choice answer for the rate is C. $\$35$, and for the equation part: $y=(25)+(35)x$