Equation for Alegbra 2

Question

Jared is building a rectangular prism garden box and wants to use soil that he already has in his shed. He decides that he wants the length of the garden box to be 2 feet longer than the width and the height to be 1 foot shorter than the width. Create an expression in terms of x, where x is the width of the garden, to demonstrate the volume of the garden box.

 

Expression:


Jared figures out that he can make the width of his garden box 3 feet long. How many cubic feet of soil does Jared have in his shed?

Answer 1

w represents the width

w + 2 represents the length

w - 1 represents the height (depth?)

w(w + 2)(w - 1) represents the volume of the box.

 

Substitute 3 for w to determine the actual volume.

Answer 2

Volume (V) = Length (L) multiplied by Width (x) multiplied by Height (H)    

 

 

 

 

V = L*x*H                                [simplify]

 

 

V = (x+2) * x * (x-1)                [L = width +2]  [Height = width -1]        

                                               [substitute values for Length and Height in terms of x, as given in the equation]

                                               [This is the final expression in terms of x]

 

 

______________________________________________________________________________________________

 

V (3+2)'*3'*(3-1)'                      [substitute numeric value for x, as given in the equation]

 

V = (5)'*3'*(2)'                          [simplify, according to Order of Operations]    

 

V = 30'                                      [multiply]

 

V = 30 cu. ft. of soil needed        [Volume is a "cubic" measurement (Length*Width*Height or Depth), as opposed to

                                                a "square" measurement such as Area (Length*Width)]