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# Allgebra Question

Posted on 2014-02-23
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I have an algebra question I cant figure out - Any help is appreciated

1. (6pts) Susan used 3  of concrete to pour a rectangular slab for a small shed on her property. If the 4-in. thick slab is 18-ft. longer than it is wide:
a) How much area ( ) does it cover in her backyard?

b) How long (ft) is each side?
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Question by:JohnMac328
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LVL 84

Expert Comment

3 what  of concrete?
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LVL 14

Expert Comment

The question seems incomplete. She used 3 what? Cubic yards, maybe? And a slab that is 18 ft longer than it is wide is not "small." Was that supposed to be 18 inches?

Anyway, here's a partial answer using 18 ft.:

Volume is H * W * L, and 4 inches = 1/3 feet, so we have this so far. (We converted inches to feet so all numbers use the same measurement.)

3 something = 1/3 * W * L

But we also know that the length is 18 ft. longer than the width, so our expression now looks like this:

3 something = 1/3 * W * (W + 18)

If that "3 something" really is cubic yards, it will need to converted to cubic feet, since the other measurements are in feet. Since 1 cubic yard is a 3ft x 3ft x 3ft cube, or 27 cubic feet, our expression becomes this:

81 cubic feet  = 1/3 * W * (W + 18)

Solve for W, and you have the width of the slab.
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Author Comment

3 yards cubed _ sorry
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Author Comment

How did you get 81?
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LVL 14

Expert Comment

3 cubic yards = 3 times a 3ft x 3ft x 3ft cube = 3 x 27 cubic feet = 81 cubic feet
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Author Comment

Ok I got w squared= 225 which w would equal 15. It is asking for ft squared so should I use 225 or 15 for the width in solving?
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LVL 84

Expert Comment

3 yards cubed = (3 * (3 ft))^3
is not the same as
3 cubic yards = 3 * ((3 ft)^3)
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Author Comment

Ok then is the equation you gave me different than what I am supposed to be  using?
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LVL 84

Expert Comment

volume = area * thickness
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Author Comment

If that "3 something" really is cubic yards, it will need to converted to cubic feet, since the other measurements are in feet. Since 1 cubic yard is a 3ft x 3ft x 3ft cube, or 27 cubic feet, our expression becomes this:

81 cubic feet  = 1/3 * W * (W + 18)

you said yards cubed is different, so how should the equation look?
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LVL 84

Expert Comment

1 yard = 3 feet
1 foot = 12 inches
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Author Comment

How should the equation look?
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LVL 84

Expert Comment

volume = area * thickness
area = width * length
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Author Comment

I am trying to help my daughter with this problem - my company does a lot of business with Expert Exchange - I am going to report you to the moderator because you are being sarcastic and not answering the questions.
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LVL 84

Expert Comment

is the volume
3 (cubic yards)
or
(3 yards) cubed
?
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Author Comment

3 yards cubed
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LVL 14

Expert Comment

Ok I got w squared= 225 which w would equal 15. It is asking for ft squared so should I use 225 or 15 for the width in solving?

Think about the reasonableness of those numbers. Although it would be a little big, a 15 ft x 33 ft slab makes sense. A 225 ft x 243 ft slab is 3 or 4 times bigger than my entire house.

Based on your insistence of "how should the equation look" I must refer you to the EE Homework Policy. You are asking us to give you the answer, without doing any thinking yourself.
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Author Comment

You said: If that "3 something" really is cubic yards, it will need to converted to cubic feet, since the other measurements are in feet. Since 1 cubic yard is a 3ft x 3ft x 3ft cube, or 27 cubic feet, our expression becomes this:

81 cubic feet  = 1/3 * W * (W + 18)

So, you then said yards cubed is different, so how should the equation look?
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LVL 14

Expert Comment

As ozo is trying to point out, "3 cubic yards" is extremely different from "3 yards cubed." One is describing 3 cubes that are each 1 yard on each side. The other is describing one large cube that is 9ft x 9ft x 9ft.

In other words, "3 yards cubed" is 9 times larger than "3 cubic yards."
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Author Comment

I know that they are completely different, how would the equation look for yards cubed? Do I do 81*9 instead?
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LVL 84

Expert Comment

The equation looks the same.
The numbers you plug in are different.
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LVL 14

Expert Comment

The only thing that the equation is missing is that the 1/3 should be 1/3 ft, like this:

81 cubic feet  = 1/3 ft * W * (W + 18)

When you reduce that to get "w squared = 225" you actually get "W squared = 225 ft squared."
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LVL 31

Expert Comment

Here is ALL the information you need to calculate:
a) How much area ( ) does it cover in her backyard? and
b) How long (ft) is each side?

1 - the thickness (or height) is 4 inches or 1/3 foot.

2 - the total volume is 3 cubic yards OR 1 yd. * 1 yd. * 1 yd.

3 - the total volume is 3 ft. * 3 ft. * 3 ft. = 27 cubic feet

4 - the VOLUME = length * width * height OR VOL = AREA * height

5 - AREA = VOL / height

6 - If one side is X feet, then AREA = X * (X + 18)
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Author Comment

paulsauve: so for the volume I got 27/4= 6.75, is that right?
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LVL 31

Expert Comment

NO - you have to have all the dimensions in the same units (either all in inches or all in feet)...

You will not get a correct answer if you divide 27 cubic feet by 4 inches!
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Author Comment

ok, area is volume/ height. So how do I covert 4in ( the height im given) to cubic feet? or vise versa?
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LVL 31

Expert Comment

If the Volume is in cubic feet, then the Width, length and height must all be in feet...

If you divide cubic feet (Volume) by height (or thickness) in FEET, then the resulting area will be in SQUARE FEET!

So, you can never get a length in inches to CUBIC FEET! The 4 inch thickness MUST be converted to feet!
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LVL 14

Expert Comment

Regardless of all the confusing responses regarding Cubic Yard vs Yards Cubed - Concrete is always sold by the cubic yard. That said -

A cubic yard is 27 cubic feet  (3*3*3)
3 cubic yards is 81 cubic feet (27*3)
If the depth is 4 inches then the Area would be 81*3  or 243 Sq Feet (4" being 1/3 ft)

Then x being the Width  then

X * (X+18) = 243

Since the only Integer that x could be would be 9

9 * (9 + 18) = 243
or 9*27 = 243
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LVL 31

Expert Comment

@ DTHConsulting

Of course you are correct - my calculation said:

2 - the total volume is 3 cubic yards OR 1 yd. * 1 yd. * 1 yd.

I should have indicated: 3 * (1 yd. * 1 yd. * 1 yd)!
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LVL 24

Expert Comment

3 yards cubed is not the same as 3 cubic yards.

3 yards x 3 yards x 3 yards = 27 cu yd = 729 cu ft
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LVL 31

Expert Comment

yes, but the presumption for this question is THREE cubic yards!
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LVL 84

Expert Comment

how do I covert 4in ( the height im given) to cubic feet?
4in / (12 in/ft) * 3 * ft * ft = ft^3
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LVL 31

Expert Comment

Sorry - 4 inches is a unit of length, you cannot convert length to volume, it is physically impossible!
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LVL 84

Expert Comment

If by convert you mean multiply by a dimensionless constant, then I agree it is physically impossible.
If you also allow multiplication by an area, then a volume of 1 cubic foot can have a base of 3 square feet and a height of 4 inches.
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LVL 14

Expert Comment

Three yards cubed -  That expression doesn't make sense - As a year is a linear expression so 3 yards cubed would be 27 linear feet - not 27 cubic yards.

If the depth was only 4"  then the area would be 27 square feet if it was 12 " thick and 81 square feet if it was only 1/3  of that

27 / (1/3)
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Author Comment

I am going to let a moderator figure out how to close this question.
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LVL 14

Expert Comment

If the Teacher who assigned this question stated(3 yards cubed)   instead of 3 Cubic Yards then the actual question is invalid.  A year is 3 feet - a yard cubed is 3ftx3ftx3ft or 9ft. Point A to Point B  it's a straight (linear) line.

There was much confusion in the responses about 3 cubic years vs 3 yards cubed.  There is not a single concrete supplier in North America who sell by anything but Cubic yards (except some in Canada who sell by the Cubic Meter)

There is only one answer to the question.
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Author Comment

Using the Quadratic Formula (which you can sing to the tune Row Row Row Your Boat) you get this

Area = 243 sq ft.

9 feet x 27 feet x 4 inches

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Author Comment

I've requested that this question be closed as follows:

Accepted answer: 0 points for JohnMac328's comment #a39883359

for the following reason:

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LVL 16

Accepted Solution

dhsindy earned 500 total points
Obviously from your comments this is either your daughter's homework or possibly a take home test question.  In this type of situation the experts are NOT allowed to give you the answer but only provide help.  You should still award the points because you received a lot of help from the experts which finally allowed you to find the answer.
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Author Closing Comment

Good point
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LVL 16

Expert Comment

The experts that provided help for you with the problem are the ones that deserve the points.  Not me.  I was only commenting on the situation - I never made a comment on the problem.
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