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December 16th, 2010, 07:12 PM   #1
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Solving For Mass, Given mass as constant and 1 unknown

So today my teacher decided to challenge us with a "word problem".

He placed an unknown amount of marbles, all of constant mass, in 8 boxes. The mass of each of these boxes are:

Box 1: 36.03 g
Box 2: 30.41 g
Box 3 = 24.93 g
Box 4 = 24.87 g
Box 5 = 20.63 g
Box 6 = 15.98 g
Box 7 = 10.43 g
Box 8 = 6.28 g

These are the values of just the MASS of the marbles. I have already subtracted the mass of the box from each one already. Now, how would you solve for the mass?

Here's what I started with:

Let's say the number of marbles is represented by 'n' (the subscripts being the # of marbles relative to a box), and 'm' being the mass of the marble (which is constant).

For example:
Mass of Marbles in Box 1 = m(n1)
Mass of Marbles in Box 2 = m(n2)
etc.

Using elimination method for each of the boxes, we isolate until we get a single variable solved. The problem is, the variable n is a set of whole numbers where n greater than or equal to 0 [of course, having 0 for n is useless I think, so I'd say it was actually greater than or equal to 1]. I have no idea how to approach this problem properly. It seems like everytime I try to isolate, there is always an unknown variable that cannot be solved.

Any ideas?
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December 16th, 2010, 07:37 PM   #2
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Re: Solving For Mass, Given mass as constant and 1 unknown

It seems to me that since 3041 (box 2) is a prime number, then the mass of each marble must be 0.01 g., but that seems really low for a marble.

On second thought, that reasoning is faulty, since it assumes the mass must be an integral multiple of 0.01 g. Never mind.
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