Question

A corner stand sells peanuts for $1.00 per pound and and walnuts for $2.00 a pound. The operator of the stand wants to make 50-pound of the peanut-walnut mix. He will maintain the cost per pound of each nut and sell the mix for $1.60 a pound. How many pounds of each type of nut should he put in the mix?

Answer 1

Let
x = number of pounds of peanuts
y = number of pounds of walnuts

(1) Now, he is selling the mix at $1.60 per pound. That means that for 50 pounds, the mix will cost (1.6 * 50)=$80

(2) Now, you now that the total number of pounds of nuts is 50 lbs.

Combining these two facts you get:
sentence (1) gives you the equation \(1x+2y=80\), since a pound of peanuts is $1, and a pound of walnuts is $2. I Drop the "1" in front of \(x\) for convenience.

sentence (2) gives you the equation: \(x+y=50\), the total number of pouns of both nuts is 50.

So you have a system of two equations:
\[\begin{cases}x+2y=80 &\\
x+y=50 &\end{cases}\]

Solve for \(x\) first in both equations and equate them:
\(x=80-2y\)
\(x=50-y\)

\(80-2y = 50 -y\)
\(80-50=y\)
\(30=y\)

Since y=30, plug this value into one of your equations, say \(x+y=50\),
\(x+30=50\)
\(x=20\)

\(\boxed{\text{solution: }x=20, y=30}\)