SOLUTION: A company mixes peanuts, cashews, and almonds to obtain 23 oz package worth 6.44 dollars. If peanuts, cashews, and almonds cost 13, 45, and 50 cents per oz respectively, and the a

Algebra ->  Matrices-and-determiminant -> SOLUTION: A company mixes peanuts, cashews, and almonds to obtain 23 oz package worth 6.44 dollars. If peanuts, cashews, and almonds cost 13, 45, and 50 cents per oz respectively, and the a      Log On


   

Question 1061254: A company mixes peanuts, cashews, and almonds to obtain 23 oz package worth 6.44 dollars. If peanuts, cashews, and almonds cost 13, 45, and 50 cents per oz respectively, and the amount of cashews is equal to the amount of almonds, how much of each is in the package?
____ oz of peanuts, _____ oz of cashews, and ____ oz of almonds.
Answer by josgarithmetic(39618) About Me  (Show Source):
You can put this solution on YOUR website!
VARIABLE    NUT           PRICE, dollars per ounce
p           peanuts         0.13
c           cashews         0.45
a           almonds         0.50

c=a

system%28p%2Bc%2Ba=23%2C0.13p%2B0.45c%2B0.5a=6.44%2Cc=a%29
Solve the system.

system%28p%2B2c=23%2C0.13p%2B0.95c=6.44%29

13p%2B95c=644
-
p=23-2c
-
Substitute for p into the cost or price equation.
13%2823-2c%29%2B95c=644
299-26c%2B95c=644
69c=644-299
69c=345
23c=115
c=115%2F23
highlight%28c=5%29-------------and you can find p and a.