SOLUTION: a candy mix is to be made by mixing candy worth $12 per kilogram with candy worth $15 per kilogram to get 120 kilograms of a mixture worth $13 per kilogram. How many kilograms of e

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Question 526457: a candy mix is to be made by mixing candy worth $12 per kilogram with candy worth $15 per kilogram to get 120 kilograms of a mixture worth $13 per kilogram. How many kilograms of each should be used ?
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let a = kgs of $12/kg candy needed
Let b = kgs of $15/kg candy needed
given:
+12a+ = cost of $12/kg candy
+15b+ = cost of $15/kg candy
+13%2A120+=+1560+ cost of mixture
-----------------------------
(1) +a+%2B+b+=+120+
(2) +12a+%2B+15b++=+1560+
Multiply both sides of (1) by 12 and
subtract (1) from (2)
(2) +12a+%2B+15b++=+1560+
(1) +-12a+-+12b+=+1440+
+3b+=+120+
+b+=+40+
and
(1) +a+%2B+b+=+120+
(1) +a+=+120+-+40+
(1) +a+=+80+
80 kgs of $12/kg candy are needed
40 kgs of $15/kg candy are needed