Question 245917: A store mixes Kenyan coffee worth $10 per kilogram and Venezuelan coffee worth $12 per kilogram. The mixture is to sell for $11 per kilogram. Find how much of each should be used to make a 360-kilogram mixture
How many kilograms of the Kenyan coffee should be in the mixture? _____ Kg
Answer by oberobic(2304)   (Show Source):
You can put this solution on YOUR website! You can start this problem thinking in terms of
K amount of Kenyan coffee @ $10 per kilogram
+ V amount of Venezuelan coffee @ $12 per kilogram
= 360 kg @ $11/kg
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The problem asks how many kg of Kenyan coffee in the mixture.
Well, it can be said the amount is 360 - V.
That is, the amount of Kenyan = known total - unknown amount of Venezuelan coffee.
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At first, this may not seem like much help. But in fact, that is one of the key ways to reduce the number of unknown variables in algebra word problems.
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K = 360 - V
V = V
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Substituting in the total cost equation:
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10*(360-V) + 12*(V) = 360*11
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Multiplying through:
3600-10V + 12V = 3960
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Collecting like terms
3600 + 2V = 3960
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Subtracting 3600 from both sides
2V = 360
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Dividing both sides by 2
V = 180
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So, V = 180, which means K = 360-180 = 180.
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We have equal amount of K and V in the total, which makes sense because we want the mixture to cost $11/kg and the two components cost $10/kg and $12/kg. $11/kg is the average.
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We can check our work by substitution back into the equation to see if our result produces the given result.
180*10 + 180*12 = 36*11
1800 + 2160 = 3960 = 36*11
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Done.
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