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Expert: Scott A Wilson - 3/7/2009


Question
Open-top boxes are made by cutting equal squares from the corners of cardboard sheets that measure 32 cm by 28 cm. Determine possible dimensions of the boxes if each has a volume of 1920 cm^3

i have come up with this equation: 1920 = x(32-2x)(28-2x)
what do i do to determine the dimensions?

Answer
Since this is an algebra problem, I would think it would have a simple answer.  Note that 32-x and 28-2x are near 30.  Also note that 30*30 = 900, which is less than half of 1,920.  Since it's less than half, we know that 2 is almost there, but also know that 2 wouldn't work.  Knowing this, let's will try 3.

That would give us 3(32-6)(28-6).
Now 32-6 = 26 and 28-6 = 22.
What we have to do is then determine what the value of 3*26*22 is.
Well, it is clear that 2*25=52, so 22*26 = 572.  Putting this back into the equation gives 3*572 = 1.716.  Nope - that's still to small.

Well, that's to small.  What now?  How about trying 4.
If we put 4 into the equation we get 4(32-8)(28-8).
Now 32-8 is 24 and 28-8 is 20.  Right here it tells me that its promising since 20 ends in a 0 and 1920 ends in 0.  Now if we calculate 4*24*20 we get 4*480.  That looks like 1,600 plus 320, which turns out to be ... 1,920 - bingo!

Isn't that what we were looking for?  

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Scott A Wilson

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I can answer any question in general math, arithetic, discret math, algebra, box problems, geometry, filling a tank with water, trigonometry, pre-calculus, linear algebra, complex mathematics, probability, statistics, and most of anything else that relates to math. I can even tell you it takes me over 2,000 steps to go a mile, but is that relevant?

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Experience in the area; I have tutored people in the above areas of mathematics for almost two years in AllExperts.com. I have tutored people here and there in mathematics since before I received a BS degree almost 25 years ago. In just two more years, I received an MS degree as well, but more on that later. I tutored at OSU in the math center for all six years I was there. Most students offering assistance were juniors, seniors, or graduate students. I was allowed to tutor as a freshman. I tutored at Mathnasium for well over a year. I worked at The Boeing Company for over 5 years. I received an MS degreee in Mathematics from Oregon State Univeristy. The classes I took were over 100 hours of upper division credits in mathematical courses such as calculus, statistics, probabilty, linear algrebra, powers, linear regression, matrices, and more. I graduated with honors in both my BS and MS degrees. Past/Present Clients: College Students at Oregon State University, various math people since college, over 7,500 people on the PC from the US and rest the world.

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My master's paper was published in the OSU journal. The subject of it was Numerical Analysis used in shock waves and rarefaction fans. It dealt with discontinuities that arose over time. They were solved using the Leap Frog method. That method was used and improvements of it were shown. The improvements were by Enquist-Osher, Godunov, and Lax-Wendroff.

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Master of Science at OSU with high honors in mathematics. Bachelor of Science at OSU with high honors in mathematical sciences. This degree involved mathematics, statistics, and computer science. I also took sophmore level physics and chemistry while I was attending college. On the side I took raquetball, but that's still not relevant.

Awards and Honors
I earned high honors in both my BS degree and MS degree from Oregon State. I was in near the top in most of my classes. In several classes in mathematics, I was first. In a class of over 100 students, I was one of the first ones to complete the test. I graduated with well over 50 credits in upper division mathematics.

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My clients have been students at OSU, people nearby, friends with math questions, and several people every day on the PC, and you're probably make one more.

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