SOLUTION: A store mixes Kenyan coffee worth 10 per kilogram and Turkish coffee worth 13 per kilogram. The mixture is to sell for 12 per kilogram. Find out how much of each should be used to

Algebra ->  Coordinate Systems and Linear Equations  -> Linear Equations and Systems Word Problems -> SOLUTION: A store mixes Kenyan coffee worth 10 per kilogram and Turkish coffee worth 13 per kilogram. The mixture is to sell for 12 per kilogram. Find out how much of each should be used to       Log On


   



Question 891351: A store mixes Kenyan coffee worth 10 per kilogram and Turkish coffee worth 13 per kilogram. The mixture is to sell for 12 per kilogram. Find out how much of each should be used to make a 504 kilogram mixture.
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 Turkish coffee needed
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(1) +a+%2B+b+=+504+ kg
(2) +%28+10a+%2B+13b+%29+%2F+504+=+12+
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(2) +10a+%2B+13b+=+12%2A504+
(2) +10a+%2B+13b+=+6048+
-------------------------
Multiply both sides of (1) by +10+
and subtract (1) from (2)
(2) +10a+%2B+13b+=+6048+
(1) +-10a+-+10b+=+-5040+
----------------------------
+3b+=+1008+
+b+=+336+
and, since
(1) +a+%2B+b+=+504+
(1) +a+=+504+-+336+
(1) +a+=+168+
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168 kg of Kenyan coffee are needed
336 kg of Turkish coffee are needed
check:
(2) +%28+10%2A168+%2B+13%2A336+%29+%2F+504+=+12+
(2) +1680+%2B+4368+=+12%2A504+
(2) +6048+=+6048+
OK