Answer
y=30
30 lbs of nuts
x=20
20 lbs of raisins
Work Step by Step
Raisins: $3.20/lb$
Nuts: $2.40/lb$
Sells 50 lbs of mixture: $2.72/lb$
x=amount of raisins (lbs)
y=amount of nuts (lbs)
$$x+y=50$$
$$3.2x+2.4y=2.72(50)$$
$$3.2x+2.4y=136$$
Rearrange the original equation to get a value for x or y.
$x+y=50$
$x=50-y$
Substitute in the 50-y for x.
$$3.2(50-y)+2.4y=136$$
$$160-3.2y+2.4y=136$$
Combine like terms.
$$160-0.8y=136$$
Subtract 136 from 160.
Then add 0.8y to the right side.
$$24=0.8y$$
Divide both sides by 0.8.
$$30=y$$
Now substitute y into the equation to find x.
$$3.2x+2.4(30)=136$$
$$3.2x+72=136$$
Subtract 72 from 136.
$$3.2x=64$$
Divide both sides by 3.2.
$$x=20$$