SOLUTION: Ground beef sells for $4.75 per kg and ground pork sells for $7.60 per kg. How many kilograms of ground pork should be mixed with 8 kg of ground beef to make a mixture that sells f

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Question 168135: Ground beef sells for $4.75 per kg and ground pork sells for $7.60 per kg. How many kilograms of ground pork should be mixed with 8 kg of ground beef to make a mixture that sells for $5.10 per kg?
Answer by gonzo(654) About Me  (Show Source):
You can put this solution on YOUR website!
problem:
Ground beef sells for $4.75 per kg and ground pork sells for $7.60 per kg. How many kilograms of ground pork should be mixed with 8 kg of ground beef to make a mixture that sells for $5.10 per kg?
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let b = kg of beef.
let p = kg of pork.
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formula to solve is:
4.75 * b + 7.60 * p = (b + p) * 5.10
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problem states that you will be using 8 kg of ground beef, so b = 8kg.
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equation becomes:
4.75 * 8 + 7.60 * p = (8 + p) * 5.10
remove parentheses on the right hand side of equation:
4.75 * 8 + 7.60 * p = 8 * 5.10 + 5.10 * p
perform indicated operations:
38 + 7.60 * p = 40.8 + 5.10 * p
subtract 38 from both sides of equation:
7.60 * p = 40.8 - 38 + 5.10 * P
subtract 5.10 * p from both sides of equation:
7.60 * p - 5.10 * p = 40.8 - 38
simplify:
(7.60 - 5.10) * p = 2.8
2.5 * p = 2.8
divide both sides of equation by 2.5:
p = 2.8 / 2.5 = 1.12 kg.
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original formula is:
4.75 * b + 7.60 * p = (b + p) * 5.10
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b = 8 (given)
p = 1.12 (solved)
formula becomes:
4.75 * 8 + 7.60 * 1.12 = (1.12 + 8) * 5.10
simplifying:
38 + 8.512 = 9.12 * 5.10
46.512 = 46.512
formula is true with values of b and p as stated.
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answer to the problem is:
1.12 kg of ground pork needs to be mixed with 8 kg of ground beef to make a mixture that sells for $5.10 per kg.