SOLUTION: Question: A store mixes Kenyan coffe worth $12 per kilogram, and Venezuelan coffee worth $16 per kilogram. The mixture is to sell for $13 per kilogram. How much of each should be

Algebra ->  Customizable Word Problem Solvers  -> Mixtures -> SOLUTION: Question: A store mixes Kenyan coffe worth $12 per kilogram, and Venezuelan coffee worth $16 per kilogram. The mixture is to sell for $13 per kilogram. How much of each should be      Log On

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Question 718014: Question:
A store mixes Kenyan coffe worth $12 per kilogram, and Venezuelan coffee worth $16 per kilogram. The mixture is to sell for $13 per kilogram.
How much of each should be used to make a 312 kilogram mixture?

Found 2 solutions by lynnlo, josmiceli:
Answer by lynnlo(4176) About Me  (Show Source):
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let +a+ = kg of Kenyan coffee needed
Let +b+ = kg of Venezuelan coffee needed
given:
(1) +a+%2B+b+=++312+
(2) +%28+12a+%2B+16b+%29+%2F+312+=+13+
----------------------------
(2) +12a+%2B+16b+=+13%2A312+
(2) +12a+%2B+16b+=+4056+
Divide through by +4+
(2) +3a+%2B+4b+=+1014+
Multiply both sides of (1) by +3+ and
subtract (1) from (2)
(2) +3a+%2B+4b+=+1014+
(1) +-3a+-+3b+=++936+
+b+=+78+
and, since
(1) +a+%2B+b+=++312+
(1) +a+=+234+
234 kg of Kenyan coffee are needed
78 kg of Venezuelan coffee are needed
check:
(2) +%28+12%2A234+%2B+16%2A78+%29+%2F+312+=+13+
(2) ++2808+%2B+1248+=+13%2A312+
(2) +4056+=++4056+
OK