If you've never heard of matrices, I don't think you'll be able to do
this so ... if this is the case, I would not waste too much time with
it. I will eventually provide you with my solution to this problem
(which uses matrices) so you will see how they can be used.

Here's the problem:

Three boys were given a bag of spitachios and they agreed to share
out the spitachios in proportion to their ages, which together
amounted to 17 1/2 years. The bag contained 770 spitachios, and for
each of four spitachios Joe took, Jack took three, and for every six
that Joe took, Jim took seven.

How many spitachios did each boy take, and what are their respective ages?



Hints (which may help or may confuse)

1. This can be reduced to 7 (linear) equations in 7 unknowns. One of the
unknowns can be determined fairly quickly and thus you can get it down
to 6 equations and 6 unknowns.

2. There is an online matrix calculator that can be used to invert
matrices and to solve matrix equations. It's at

http://www.bluebit.gr/matrix-calculator/

Matrices are used to solve the generalization of 1-equation / 1-unknown
problems.

ax = b

where a and b are constants and x is the unknown.

The solution is

x = (1/a)b

The generalization is:

Ax = b

where A is an nxn matrix of constants, x is an nx1 matrix (vector) of
unknowns and b is an nx1 matrix (vector) of constants.

This is solved by

x = (1/A)b

where 1/A stands for the inverse matrix for A and the product on the
right is a matrix product.

- Lee