College Algebra Question

Question

A store sells cashews for $7.00 per pound and peanuts for $1.00 per pound. The manager decides to mix 37 pounds of peanuts with some cashews and sell the mixture for $3.00 per pound. How many pounds of cashews should be mixed with the peanuts so that the mixture will produce the same revenue as selling the nuts separately?

Answer 1

Hi Rachel! The hint here is that the mixture has to produce the SAME or = revenue as selling separately, so...

If C = pounds of cashews and P = pounds of peanuts....

$7.00 C + $1.00 P = amount you earn if you sell them separately

$3.00 (C + P) = amount you earn if you sell the mix...in this case the manager wants to use P = 37

So set them equal to each other $7.00 C + $1.00 P = $3.00 (C + 37), and sub 37 for P to solve for C