A contractor orders 8 cubic yards of premixed cement, all of which is to be used to pour a rectangular 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?
NOTE: 1 cubic yard = 27 cubic feet
Below is your answer followed by my reply in brackets.
Your said:
Let the width of the patio be W (ft), then the volume will be:
V=W*(2W)*(1/3) cubic ft,[What part of the question indicated that we are dealing with volume?]
so:
(2/3)W^2 = 8*27 cubic ft,
so:
W=sqrt(8*27*3/2)=18 ft{Why did you take the square root?]
so the patio is 18 by 36 ft.
We are given the amount of cement ordered in cubic yards, which is a
volume, and this will be the the volume of the patio when laid.
we have from the previous equation:so:
(2/3)W^2 = 8*27 cubic ft,
so:
W=sqrt(8*27*3/2)=18 ft{Why did you take the square root?]
(2/3)W^2 = 8*27,
so:
W^2=8*27*3/2,
the term on the left of this is W squared, so to get W we need to take
square roots, so:
W=sqrt(8*27*3/2)=18
RonLso the patio is 18 by 36 ft.
I can see from your reply that it's super important to pay attention to detail in terms of word problems, right? Every word leads to a clue.
Of course, this does NOT take away the fact that there are word problems that are simply complicated in nature.
I thank you very much.