word problems

Question

Melanie recently hired a plumber to do some necessary work. On the final bill, Melanie was charged a total of $760. $480 was listed for parts and the rest for labor. If the hourly rate for labor was $70, how many hours of labor was needed to complete the job?

(A) First write an equation you can use to answer this question. Use
x
as your variable.

The equation is


(B) Solve your equation in part (A) to find the number of labor hours needed to do the job.

Answer: The number of labor hours was .

Answer 1

Pretend you went took a taxi, and they charged you a base fee of $5 just to get in.  Then, they charged $2 for every mile they drove.  So if you drove 1 mile, it would be 2(1) = 2.  If you drove 4 miles, 2(4) = 8.  If you drove x miles, 2x.  

 

If you were to make an equation with x for the number of miles, you would have

 

total cost = base fee + cost of miles

 

C = 5 + 2x  

 

 

Now in your case, you have a "base fee" of $480.  This amount is what you paid for parts, it doesn't change. The cost for labor changes though, depending on how many hours is spent working.  If the rate is $70 per hour, 1 hour is 70(1), 2 hours is 70(2), x hours is 70x. 

 

 

total cost = base fee + cost of labor

 

 

 

The problem also told you how much it cost you in total, $760.  Plug these all in now!

 

 

 

 

Once you have that equation, solve for the number of hours, x by isolating it. 

Answer 2

70(hours worked) = (total price - parts price)

 

70x = 760-480

70x = 280

x = 4 hours