Question

How many pounds of cashew nuts worth 75 cents a pound must be mixed with 10 pounds of pecans worth $1.50 a pound to make a mixture worth $1.00 a pound? Which of the equations could be used to solve for p, the pounds of cashew nuts?

Answer 1

Let c represent the weight of cashews and p the weight of pecans.

Then c + 10 = total weight of the nut mixture.

An equation for the value of the mixture follows:

 $1.50(10 lb) + $0.75c = (c+10)($1.00)

Solve this equation for c:  15 + .75c = c + 10.  Subtract .75c from both sides:

15 = 1c - 0.75c + 10.  Then 5=0.25c, and c = 5/0.25, or 20.

Need 20 lb of cashews.


Check:  the pecans weigh 10 lb and are worth $1.50 per lb, so the total value of the pecans is $15.  The total value of the cashews is (20 lb)($0.75/lb), or $15.     Does (20 lb + 10 lb)($1/lb) = $15 + $15?  Yes.  So c= 20 lb is correct.