Question 193138: A nut wholesaler sells a mix of peanuts and cashews. The wholesaler charges $2.80 per pound for peanuts and $5.30 per pound for cashews. The mix is to sell for $3.30 per pound. How many pounds of peanuts and how many pounds of cashews should be used to make 100 pounds of the mix?
An adult pass for a country fair costs $2 more than a children’s pass. When 378 adult and 214 children’s passes were sold, the total revenue was $2384. Find the cost of an adult pass
Answer by jonvaliente(64)   (Show Source):
You can put this solution on YOUR website! Problem #1: Nuts!
Let p=no of pounds of peanuts
c=no of pounds of cashews
To sell for $3.30 per pound for a 100-pound mix. The total value of the mix should be $3.30 x 100 = $330, so from here we get:
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2.80*p + 5.30*c = 330 (1)
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We also know that the total mix is 100 pounds, so:
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p + c = 100 (2)
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Let's express p in terms of c, so:
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p = 100 - c
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Substitute this value in (1):
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2.80*(100-c) + 5.30*c = 330
280 - 2.80c + 5.30c = 330
280 + 2.50c = 330
2.50c = 330 - 280
2.50c= 50
c = 50/2.50
c=20
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So we need 20 pounds of cashew nuts and 100-c=100-20=80 pounds of peanuts!
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Problem #2: Country Fair
Let x = cost of a children's pass
. x+2 = cost of an adult pass ("An adult pass...costs $2 more than a children's pass)
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So:
378*(x+2)+214*x = 2384
378x + 756 + 214x = 2384
592x + 756 = 2384
592x=2384-756
592x=1628
x = 1628/592
x=2.75
So if a children's pass costs $2.75, then an adult pass=x+2=2.75+2=$4.75
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