SOLUTION: Peanuts cost $2.50 per pound, almonds cost $6.50 per pound , and cashews cost $8 per pound . How many pounds of peanuts and cashews should be added to one pounds of almonds to obta

Algebra ->  Coordinate Systems and Linear Equations  -> Linear Equations and Systems Word Problems -> SOLUTION: Peanuts cost $2.50 per pound, almonds cost $6.50 per pound , and cashews cost $8 per pound . How many pounds of peanuts and cashews should be added to one pounds of almonds to obta      Log On


   

Question 840132: Peanuts cost $2.50 per pound, almonds cost $6.50 per pound , and cashews cost $8 per pound . How many pounds of peanuts and cashews should be added to one pounds of almonds to obtain a six-pound mixture at $5 per pound?
Answer by josgarithmetic(39616) About Me  (Show Source):
You can put this solution on YOUR website!
p pounds of peanuts
c pounds of cashews
1 pound of almonds
WANTED: Mixture of 6 pounds

Account for cost of the mixture:
2.5p%2B6.5c%2B8%2A1=%281%2Bp%2Bc%29%2A5, which uses two variables, p and c.

Account for pounds of the mixture:
1%2Bp%2Bc=6, which again uses just those two variables.

SIMPLIFY EACH EQUATION

2.5p%2B6.5c%2B8=5%2B5p%2B5c
5p%2B5c%2B5=2.5p%2B6.5c%2B8
2.5p-1.5c=3
5p-3c=6 Cost Equation

p%2Bc%2B1=6
p%2Bc=6-1
p%2Bc=5 Poundage Equation

SOLVE THIS SYSTEM FOR p AND c
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5p-3c=6
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p+c=5
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The HARD PART was analyzing, setting up the equations, and finding the system of equations to solve. You do the rest.