SOLUTION: A merchant has coffee worth $30 a pound that she wishes to mix with 30 pounds of coffee worth $80 a pound to get a mixture that can be sold for $60 a pound. How many pounds of the

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Question 589084: A merchant has coffee worth $30 a pound that she wishes to mix with 30 pounds of coffee worth $80 a pound to get a mixture that can be sold for $60 a pound. How many pounds of the $30 coffee should be used?
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let x = pounds of $30/pound coffee needed
+30%2A80+=+2400+ = cost in dollars of $80/pound coffee
+%28+30x+%2B+2400+%29+%2F+%28+x+%2B+30+%29+=+60+
+30x+%2B+2400+=+60%2A%28+x+%2B+30+%29+
+30x+%2B+2400+=+60x++%2B+1800+
+30x+=+2400+-+1800+
+30x+=+600+
+x+=+20+
20 pounds of $30/pound coffee is needed
check:
+%28+30x+%2B+2400+%29+%2F+%28+x+%2B+30+%29+=+60+
+%28+30%2A20+%2B+2400+%29+%2F+%28+20+%2B+30+%29+=+60+
+%28+600+%2B+2400+%29+%2F+50+=+60+
+3000+=+60%2A50+
+3000+=+3000+
OK