SOLUTION: If one blend of coffee sells for $9.00 per pound and another blend sells for $8.00 per pound how many of each type should be used to maake a 20 pond blend that sells for $8.40 per

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Question 522918: If one blend of coffee sells for $9.00 per pound and another blend sells for $8.00 per pound how many of each type should be used to maake a 20 pond blend that sells for $8.40 per pound?
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let a = pounds of $9 coffee needed
Let b = pounds of $8 coffee needed
given:
(1) +a+%2B+b+=+20+
(2) +%289a+%2B+8b%29+%2F+20+=+8.4+
----------------------
(2) +%289a+%2B+8b%29+%2F+20+=+8.4+
(2) +9a+%2B+8b+=+20%2A8.4+
(2) +9a+%2B+8b+=+168+
Multiply both sides of (1) by 8 and
subtract (1) from (2)
(2) +9a+%2B+8b+=+168+
(1) +-8a+-+8b+=+160+
+a+=+8+
and, since
(1) +a+%2B+b+=+20+
(1) +8+%2B+b+=+20+
(1) +b+=+12+
8 pounds of $9 coffee are needed
12 pounds of $8 coffee are needed
check:
(2) +%289a+%2B+8b%29+%2F+20+=+8.4+
(2) +%289%2A8+%2B+8%2A12%29+%2F+20+=+8.4+
(2) +%2872+%2B+96%29+=+8.4%2A20+
(2) +168+=+168+
OK