SOLUTION: A coffee distributor needs to mix a(n) Kona coffee blend that normally sells for $8.80 per pound with a Kenya coffee blend that normally sells for $14.00 per pound to create 100 po

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Question 569509: A coffee distributor needs to mix a(n) Kona coffee blend that normally sells for $8.80 per pound with a Kenya coffee blend that normally sells for $14.00 per pound to create 100 pounds of a coffee that can sell for $13.17 per pound. How many pounds of each kind of coffee should they mix?
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let +a+ = pounds of Kona coffee needed
Let +b+ = pounds of Kenya coffee needed
given:
(1) +a+%2B+b+=+100+
(2) +%28+8.8a+%2B+14b+%29+%2F+100+=+13.17+
------------------------------
(2) +8.8a+%2B+14b+=+1317+
(2) +88a+%2B+140b+=+13170+
Multiply both sides of (1) by +88+
and subtract (1) from (2)
(2) +88a+%2B+140b+=+13170+
(1) +-88a+-+88b+=+-8800+
+52b+=+4370+
+b+=+84.038+
and
(1) +a+%2B+84.038+=+100+
(1) +a+=+15.962+
15.962 pounds of Kona coffee are needed
84.038 pounds of Kenya coffee are needed
check:
(2) +%28+8.8a+%2B+14b+%29+%2F+100+=+13.17+
(2) +%28+8.8%2A15.962+%2B+14%2A84.038+%29+%2F+100+=+13.17+
(2) +%28+140.466+%2B+1176.532+%29+%2F+100+=+13.17+
(2) +1316.998+=+1317+
close enough