Math question !! need help ASAP !!!

Question

nets nets store sells cashew for six dollars per pound and peanuts for 4.50 a pound. How much of each must be mixed to get 20 pounds of a mixture that can be sold for five dollars a pound

Answer 1

Let

c = # of pounds of cashews

p = # of pounds of peanuts

c & p are the unknowns

The goal is to have (1/20)(6c + 4.5p) = 5

In words: the price per pound of 20lbs of mixture is supposed to be $5.00

So far there is one equation in two unknowns, therefore we need a 2nd equation. We get that 2nd equation from the desired weight of the mixture: p + c = 20

Using these two equations, you can solve (say by substitution, or elimination of a variable) for p = 40/3 (approx 13.333) lbs , c = 20/3 (approx 6.667) lbs

Check:

Using the weight equation: p + c = 40/3 + 20/3 = 60/3 = 20 (ok)

Also, make sure the cost/lb equation is ok:

(1/20)(6c + 4.5p) = (1/20)(6(20/3) + 4.5(40/3)) = (1/20)(40 + 60) = (1/20)(100) = 5 (ok)