SOLUTION: a company wants to mix 25 pounds of peanuts worth $3 a pound with cashews worth $6 a pound in order to make an experimental mix worth $4.50 a pound. How many pounds of cashews shou

Question 511163: a company wants to mix 25 pounds of peanuts worth $3 a pound with cashews worth $6 a pound in order to make an experimental mix worth $4.50 a pound. How many pounds of cashews should be added to the peanuts?
Found 2 solutions by Alan3354, Maths68:
Answer by Alan3354(69443) (Show Source): You can put this solution on YOUR website!
$4.50 is the average, so it's equal amounts.
25 pounds
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I wouldn't call that an experiment.

Answer by Maths68(1474) (Show Source): You can put this solution on YOUR website!
Cashew=c
Total cost of Cashews=$6c
Peanuts=25 lb
Total cost of Peanuts=3*25=$75
Mixture=m lb
Total cost of mixture = $4.50(m)
=================================================================
Cashew+Peanuts=mixture
c+25=m
c=m-25................(1)
================================================================
Total cost of Cashews+Total cost of Peanuts=Total cost of mixture
6c+75=4.50m
6c=4.50m-75
6c/6=(4.50m-75)/6
c=(4.50m-75)/6...........(2)
================================================================
Put the value of c from (1) to (2)
c=(4.50m-75)/6...........(2)
m-25=(4.50m-75)/6
6(m-25)=4.50m-75
6m-150=4.50m-75
6m-4.50m=-75+150
1.5m=75
1.5m/1.5=75/1.5
m=50
Put the value of m in (1)
c=m-25................(1)
c=50-25
c=25
================================================================================
Cashew=c = 25lb
Total cost of Cashews=$6c = 6*25= $150
Peanuts=25 lb
Total cost of Peanuts=3*25=$75
Mixture=m lb = 50 lb
Total cost of mixture = $4.50(50)=$225
===============================================================================
Check
Cashew(lb)+Peanuts(lb)=mixture(lb)
25+25=50
50 lb =50 lb
Total cost of Cashews+Total cost of Peanuts=Total cost of mixture
6*25+3*25=4.5*50
150+75=225
225=225

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