Price of the door?

Question

The cost of labor for installing a door was $75 less than the price of the door, itself. If the total cost of the project was $375, what was the price of the door? 

 

a. What is the general relationship among door prices, labor and total?

 

b. If the door price were $140 and the labor is $75 less than the door price, find the labor cost and total cost.

 

c. You want to know what number would go in place of $140 in order to get a total of $375. Write an equation with D in place of $140 and $375 in place of your answer to part b. 

 

d. Solve your equation for D.

 

e. For the door cost found in part d, find the labor cost and show that your answers satisfy the conditions stated in the original problem.

Answer 1

Hi Cierra

 

The cost of the project is the sum of the material (Door) cost and Labor. If we call D the cost of the door, and L the installation labor, we have:

 

D + L = $375   (1)

 

Also, we know that the labor was $75 less than the cost of the door. In other words,  L = D - $75   (2)

 

Let's substitute (2) into (1):   D + (D - $75) = $375

 

                                          2D = $375 - $75 = $300     resulting   D = $150

 

(a)  Total = Door price + Labor   or   T = D + L  where T is the total

 

(b)  D= $140   L = $140 - $75 = $65     T = D + L =  $205

 

(c)  T = D + L  

     

     $375 = D + (D - $75)

 

     $375 = 2D - $75

 

      D = ($375 + $75)/2

 

(d) Solvind D from (c):   D = $225   The cost of the Door should be $225 to get a total of $375

 

     D =