|Dec 11, 2012, 06:29 PM||#1|
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...
|Dec 11, 2012, 06:49 PM||#4|
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?
|Dec 11, 2012, 06:56 PM||#5|
EDIT: HINT 2: It helps to also write the units down. This way you don't try to equate $ and cubic feet.
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|Dec 11, 2012, 06:58 PM||#6|
|Dec 11, 2012, 07:06 PM||#7|
|Dec 11, 2012, 07:11 PM||#8|
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.
|Dec 11, 2012, 11:10 PM||#10|
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