Question 1139813
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There are constraint equations for fiber, protein, and fat.<br>
fiber: {{{25x+100y+275z+100w = 3950}}}
protein: {{{30x+80y+210z+80w = 3060}}}
fat: {{{30x+70y+190z+60w = 2740}}}<br>
That's a system of three equation in four unknowns; it will have (if the problem is well formulated) a family of solutions in non-negative integers.<br>
Solving the system algebraically would be very tedious.  A solution using matrices on a graphing calculator produces the following set of equations relating w, x, y, and z:<br>
x-w = 0
y+4w = 12
z-w = 10<br>
Use those equations to express x, y, and z in terms of w; then substitute the values shown for w to find the different ways the breeder can get the right amounts of fiber, protein, and fat.<br>
Note: The problem as you state it says there are four ways to get the right amounts, but it seems to be asking for only the solutions where w is 0, 1, or 2.  There is in fact a fourth value of w that provides a solution.