Advanced Math/Capacity

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Question
A man has a barrel which is full of vinegar.  He removes 4 gallons and refills the barrel with water. He then removes 8 gallons.  An original vinegar amount of 21 gallons remains in the barrel.  Calculate capacity of barrel.  Thanks.

Answer
"A man has a barrel which is full of vinegar."
The barrel contains v gallons of vinegar.

"He removes 4 gallons and refills the barrel with water."
The barrel contains 4 gallons of water and (v-4) gallons of vinegar.
(v-4)/v of the contents of the barrel is vinegar.

"He then removes 8 gallons."
(v-8) gallons of liquid remains.

"An original vinegar amount of 21 gallons remains in the barrel."
(v-4)/v of (v-8) gallons = 21 gallons
(v-4)/v (v-8) = 21
(v - 12v + 32)/v = 21
(v - 12v + 32) = 21v
v - 33v + 32 = 0

By the quadratic formula,
v= [33 √(33 4132)] / [21]
 = [33 √961] / 2
 = [33 31] /2
 = 1, 32
1 is an extraneous solution
v = 32
The barrel holds 32 gallons.

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Janet Yang

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I can answer questions in Algebra, Basic Math, Calculus, Differential Equations, Geometry, Number Theory, and Word Problems. I would not feel comfortable answering questions in Probability and Statistics or Topology because I have not studied these in depth.

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I tutor students (fifth through twelfth grades) and am a Top Contributor on Yahoo!Answers with over 24,000 math solutions.

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