Question 127917
The question is asking "how many pounds of each should she buy?"  That tells us what our variables should be.
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x=pounds of peanuts
y=pounds of fancy nuts
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x + y = 13                    (equation 1)
3.50x + 7.50y = 85.50         (equation 2)
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Solve this system of equations.  I'll do it by substitution here.

From equation 1,   y = 13 - x.
By substitution into equation 2, 3.50x + 7.50(13 - x) = 85.50
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Solving for x we get x=3.
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Substitute 3 for x into equation 1 to solve for y, and y=13.