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Old Dec 11, 2012, 06:29 PM   #1
imaketouchtheme
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Math Halp!

So, after being out of traditional classroom math for over two years now, I'm starting to struggle with basic word problems. I'm taking an online practice exam for my upcoming math class, and I cannot figure out the answer to this question.

"A rectangular box with volume 360 cubic feet is built with a square base and top. The cost is $1.50 per square foot for the top and the bottom and $2.00 per square foot for the sides. Let x represent the length of a side of the base. Express the cost the box as a function of x."

Thanks for any help...
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Old Dec 11, 2012, 06:35 PM   #2
r.j.s
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(1.5x^2)(2y)=360 is a good start for you.
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Old Dec 11, 2012, 06:41 PM   #3
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Quote:
Originally Posted by r.j.s View Post
(1.5x^2)(2y)=360 is a good start for you.
wouldn't it be

2*(1.5x^2)+4*2(x*y) = 360

where x is the length and width and y is the depth?
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Old Dec 11, 2012, 06:49 PM   #4
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In situations like this drawing a picture might help.

You know that you've got the top and bottom of your box and these are squares of area x times x or x^2. They in total have area 2x^2 and so the cost of the top and bottom is that times $1.5 I.e. 1.5(2x^2) or 3x^2

The sides are each of area x times the vertical, which I'll call y, and there are four of them, 4(xy), cost 2 a sq ft so 8xy.

The total cost is $360 which = 3x^2 + 8xy At this point I'm puzzled as this differs from what was suggested first above... Still, I've shown my working so am confident(!)

I suspect r.j.s. was thinking about volumes in a muddled sort of way?
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Old Dec 11, 2012, 06:56 PM   #5
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Quote:
Originally Posted by leighonigar View Post
The total cost is $360
O RLY?



Quote:
Originally Posted by imaketouchtheme View Post
A rectangular box with volume 360 cubic feet
HINT: the volume of the box is a function of x and y which allows you to express y as a function of x. Stick that back in the formula for the cost of the box.

EDIT: HINT 2: It helps to also write the units down. This way you don't try to equate $ and cubic feet.

B
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Old Dec 11, 2012, 06:58 PM   #6
leighonigar
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Quote:
Originally Posted by balamw View Post
O RLY?





HINT: the volume of the box is a function of x and y which allows you to express y as a function of x. Stick that back in the formula for the cost of the box.

B

Good times for a change! Thanks for that :-)
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Old Dec 11, 2012, 07:06 PM   #7
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Quote:
Originally Posted by leighonigar View Post

I suspect r.j.s. was thinking about volumes in a muddled sort of way?
I forgot to double and was don't know why I forgot the x for the sides ...

I shouldn't do maths on morphine.
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Old Dec 11, 2012, 07:11 PM   #8
leighonigar
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Quote:
Originally Posted by r.j.s View Post
I forgot to double and was don't know why I forgot the x for the sides ...

I shouldn't do maths on morphine.
I wouldn't worry, I misread the question so was at least as muddled... !

Anyway, it is actually possible now with balamw's insight.

The formula I derived above is for cost, but we need to get rid of y.

As the formula for the volume of the box which we know(!) is x.x.y then x^2y = 360

Rearranging we get a formula for y which we can substitute back in.

Last edited by leighonigar; Dec 11, 2012 at 07:17 PM.
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Old Dec 11, 2012, 07:16 PM   #9
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I have 'people' for that type of thing.
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Old Dec 11, 2012, 11:10 PM   #10
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Originally Posted by r.j.s View Post
I shouldn't do maths on morphine.
That should be the title of an xkcd cartoon.

Or a series of cartoons: I shouldn't do ____ on morphine. Kinda like his "My hobby" series.
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Old Dec 11, 2012, 11:13 PM   #11
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ALWAYS ALWAYS ALWAYS draw a picture. Start there, then brute logic your way through it.
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