A store sells cashews for $ 6.00

Question

A store sells cashews for $ 6.00 per pound and peanuts for $ 3.00 per pound. The manager decides to mix x pounds of cashews with y pounds of peanuts to make a 60  pound mixture of mixed nuts and sell the mixture for $ 5.00 per pound. How many pounds of cashews and how many pounds of peanuts should be mixed together so that the mixture will produce the same revenue as would selling the nuts separately?

Answer 1

We have x = cashew pounds and y = peanut pounds. Here's what we know:

x + y = m (We have poundage of mixed nuts)

6x + 3y = 5m (those pounds costs averages to $5 mixed)

m = 60 (we're told we have 60 pounds of mixed nuts)

 

Plug in 60 for m:

x + y = 60
6x + 3y = 5 * 60

6x + 3y = 300

 

We now have our system of equations. Let's use elimination by multiplying the first equation by -3:

-3x - 3y = -180

6x + 3y = 300

--------------------

3x = 120

x = 40

 

You should be able to find the peanuts from here and check the work.