SOLUTION: A contractor orders 8 cubic yards of premixed cement,all of which is to be used to pour a patio that will be 4 inches thick. If the length of the patio is specified to be twice the

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Question 1207447: A contractor orders 8 cubic yards of premixed cement,all of which is to be used to pour a patio that will be 4 inches thick. If the length of the patio is specified to be twice the width, what will be the patio dimensions? (1 cubic yard 27 cubic feet)

Seeking the set up equation(s).
Found 3 solutions by josgarithmetic, ikleyn, Theo:
Answer by josgarithmetic(39617) About Me  (Show Source):
You can put this solution on YOUR website!
4 inches thick is 1%2F3 feet thick.

8%28yd%5E3%29%2A27%28ft%5E3%2Fyd%5E3%29=%2827%2F8%29ft%5E3, amount of premixed cement available.

DIMENSIONS
2w, length
w, width
1%2F3 thick

If assume all the premix is to be used for the patio then
%281%2F3%292w%5E3=27%2F8
Solve for w.
This is all in unit of feet.

Answer by ikleyn(52780) About Me  (Show Source):
You can put this solution on YOUR website!
.
A contractor orders 8 cubic yards of premixed cement, all of which is to be used
to pour a patio that will be 4 inches thick. If the length of the patio is specified
to be twice the width, what will be the patio dimensions? (1 cubic yard 27 cubic feet)
~~~~~~~~~~~~~~~~~~~~~~ 

The volume of 8 cubic yards is 8*27 cubic feet, or  8%2A27%2A12%5E3 cubic inches.

The area covered by the premixed cement is the volume divided by thickness, or

    %288%2A27%2A12%5E3%29%2F4 = 2*27 = 93312 square inches.


If the width is W, then the length is 2W, according to the problem.

So, the area equation is

    W * (2W) = 93312  square inches,  or

    2W^2 = 93312 

    W^2 = 93312/2 = 46656

    W = sqrt%2846656%29 = 216 inches = 18 feet.


ANSWER.  The dimensions are 18 feet (the width) by 2*18 = 36 feet (the length).

Solved, with full explanations.



Answer by Theo(13342) About Me  (Show Source):
You can put this solution on YOUR website!
volume = length * width * depth.
let W = width and L = length and D = depth.
let V = volume
you get V = L * W * D
you are given that L = 2W, so replace L with 2W.
if you have trouble working it from there, let me know.
make sure you convert everything to the same measure.
theo