High school track: 24 placers earn 108 points, allocated as follows; 7points for first(f) , 4 for second(s) , and 1 for third(t) . School's second placers total it's first and third placers.
This string of data can be arranged into three equations:
{7f + 4s + t= 108}
{f + s + t= 24}
{-f + s - t= 0} simplified by the inverse of addition, subtraction, from {f + t= s}
From these equations, a matrix arises: [7 4 1 108]
[1 1 1 24]
[-1 1 -1 0]
Which, using the reduced-row-echelon-form function yields: 8 first placers, 12 second placers, and 4 third placers. {8 + 4= 12} 12*4 + (7*8) + 4= 108
"The night will last, forever!" ~ Nightmare Moon
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