An electrician charges a set fee of $50 for every house call and then charges an additional hourly rate. One day, the electrician earned a total of $400 for a 5 hour job. Write an equation for C, in terms of t, representing the total cost of the electrician's services if the electrician spends t hours at the house working.

Question

An electrician charges a set fee of $50 for every house call and then charges an additional hourly rate. One day, the electrician earned a total of $400 for a 5 hour job. Write an equation for C, in terms of t, representing the total cost of the electrician's services if the electrician spends t hours at the house working.

Answer 1

The total cost C of the electrician's services can be represented by the equation:

C = 50 + t * hourly rate

Since the electrician earned $400 for a 5-hour job, we can substitute these values into the equation:

400 = 50 + 5 * hourly rate

Simplifying the equation, we have:

400 - 50 = 5 * hourly rate

350 = 5 * hourly rate

Dividing both sides by 5, we find:

hourly rate = 350 / 5 = 70

Therefore, the equation for C, in terms of t, is:

C = 50 + 70t

Answer 2

The total cost (C) of the electrician's services consists of the fixed fee of $50 and the additional hourly rate. Let's assume the hourly rate is $x.

For each hour the electrician spends working (t), the additional cost is x * t.

So the equation for C, in terms of t, would be:
C = 50 + x * t

Answer 3

To write an equation for C, the total cost of the electrician's services in terms of t, you need to consider the fixed fee of $50 for every house call and the additional hourly rate.

Let's break it down:

1. The fixed fee for every house call is $50.
2. The electrician also charges an additional hourly rate.

Since we know that the electrician earned a total of $400 for a 5-hour job, we can use this information to find the additional hourly rate:

Total earnings = Fixed fee + Additional hourly rate * t

$400 = $50 + Additional hourly rate * 5

To solve for the additional hourly rate, subtract $50 from both sides of the equation:

$400 - $50 = Additional hourly rate * 5

$350 = Additional hourly rate * 5

Divide both sides of the equation by 5 to isolate the variable:

Additional hourly rate = $350 / 5

Additional hourly rate = $70

Now, with the additional hourly rate, we can write the equation for C, the total cost of the electrician's services in terms of t:

C = $50 + ($70 * t)

Therefore, the equation is: C = 50 + 70t.