Solving for Mass, Given Mass as Constant + Infinite # of Discrete Unknown variables)
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
Total mass = 169.56 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).
Mass of Marbles in Box 1 = m(n1)
Mass of Marbles in Box 2 = m(n2)
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 (in other words, discrete) 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 every time I try to isolate, there is always an unknown variable that cannot be solved.
Any ideas? I would like for you guys to use the same variables I've used, but if it helps to use other variables instead, that'll be fine.