Question

mckirnan Brothers went to introduce a special mixture of chocolate covered pretzels and chocolate covered peanuts the plan is to mix 12 lb of the mixture at a time to be sold for $3 a pound the price of stuff for $2.75 a pound of peanuts for $3.50 how many pounds of each should be in the mixture

Answer 1

There is surely a typo in there somewhere as reading it gave me a headache :D

I believe it was intended to say that a pound of peanuts is $3.5 and a pound of covered peanuts is $2.75.  Then we are to make a 12 pound mixture worth $3 a pound.

Let p be the pounds of peanuts and c be the pound of chocolate covered peanuts.  Then:

(2.75p+3.5c)/12=3, given that p+c=12, c=12-p, making the equation become:

(2.75p+3.5(12-p)/12=3,  multiply both sides by 12

2.75p+42-3.5p=36  combine like terms on left side

-0.75p+42=36  subtract 42 from both sides

-0.75p=-6  divide both sides by -0.75

p=8 lb, since c=12-p

c=4 lb

So the brothers should mix 8 pounds of regular peanuts with 4 pounds of chocolate covered peanuts to produce a 12 pound mixture worth $3 per pound.