SOLUTION: In an experiment involving mice, a zoologist needs a food mix that contains, among other things, 23 grams of protein, 6.2 grams of fat, and 16 grams of moisture. She has on hand mi

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Question 885880: In an experiment involving mice, a zoologist needs a food mix that contains, among other things, 23 grams of protein, 6.2 grams of fat, and 16 grams of moisture. She has on hand mixes of the following compositions: Mix A contains 20% protein, 2% fat, and 15% moisture; Mix B Contains 10% protein, 6% fat, and 10% moisture; and Mix C Contains 15% protein, 5% fat, and 5% moisture. How many grams of each mix should be used to get the desired diet mix? Answer and Solution please.
Answer by josgarithmetic(39617) (Show Source):
You can put this solution on YOUR website!
How much of the mix does the zoologist want? Call this Q.

These are in grams:
x = how much of A
y = how much of B
z = how much of C

PROTEIN:
FAT:
MOISTURE:

Three linear equation in three unknowns. The simplification to do is multiply each equation's left and right members by 20. That will ALMOST give the system of equations with whole number coefficients.

EQUIVALENT SYSTEM:

Not quite simple enough.. Multiply the "124" equation by

EQUIVALENT SYSTEM:

A possible way for Elimination is solve eq.2 for z and solve eq.3 for z. This gives you two linear equations in x and y. Solve THIS system for x and y. Having the values now for x and y, use them (in equation 1) to solve for and find the value for z.

NOW you can solve the system either by Elimination Method or with matrix row operations.