SOLUTION: A merchant wishes to mix two grades of peanuts costing $3 and $4 per pound, respectively, with cashews costing $8 per pound, to obtain 140 pounds of a mixture costing $6 per pound.

Algebra ->  Matrices-and-determiminant -> SOLUTION: A merchant wishes to mix two grades of peanuts costing $3 and $4 per pound, respectively, with cashews costing $8 per pound, to obtain 140 pounds of a mixture costing $6 per pound.      Log On


   

Question 1029941: A merchant wishes to mix two grades of peanuts costing $3 and $4 per pound, respectively, with cashews costing $8 per pound, to obtain 140 pounds of a mixture costing $6 per pound. If the merchant also wants the amount of cheaper-grade peanuts to be twice that of the better-grade peanuts, how
many pounds of each variety should be mixed?
Answer by josgarithmetic(39617) About Me  (Show Source):
You can put this solution on YOUR website!
z for cashews
x and y for the peanuts, cheap and expensive in that order
x%2Fy=2
from which
x=2y


Poundage: x%2By%2Bz=140

Mixture Price: %283x%2B4y%2B8z%29%2F%28140%29=6

Make the substitution for x, and simplify into the TWO variable system:
system%283y%2Bz=140%2C10y%2B8z=6%2A140%29
further simplifiable to
highlight%28system%283y%2Bz=140%2C5y%2B4z=420%29%29-------------solve this system for y and z, and then find x from the earlier given equation from the description.