SOLUTION: I need help with This question: How many pounds of regular Coffee that sells for $4 per pound and how many pounds of premium coffee that sells for $8 should be blended to obtain

Algebra ->  Customizable Word Problem Solvers  -> Finance -> SOLUTION: I need help with This question: How many pounds of regular Coffee that sells for $4 per pound and how many pounds of premium coffee that sells for $8 should be blended to obtain      Log On

Ad: Over 600 Algebra Word Problems at edhelper.com


    

Question 995253: I need help with This question:
How many pounds of regular Coffee that sells for $4 per pound and how many pounds of premium coffee that sells for $8 should be blended to obtain 24 pounds of a gourmet blend that sells for $6 per pound?
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let +a+ = pounds of regular coffee needed
Let +b+ = pounds of premium coffee needed
-----------------
(1) +a+%2B+b+=+24+
(2) +%28+4a+%2B+8b+%29+%2F+24+=+6+
------------------------
(2) +4a+%2B+8b+=+144+
(2) +a+%2B+2b+=+36+
--------------------
Subtract (1) from (2)
(2) +a+%2B+2b+=+36+
(1) +-a+-+b+=+-24+
------------------
+b+=+12+
and
(1) +a+%2B+12+=+24+
(1) +a+=+12+
12 pounds of regular coffee are needed
12 pounds of premium coffee are needed
check:
(2) +%28+4a+%2B+8b+%29+%2F+24+=+6+
(2) +%28+4%2A12+%2B+8%2A12+%29+%2F+24+=+6+
(2) +%28+48+%2B+96+%29+%2F+24+=+6+
(2) +144+=+6%2A24+
(2) +144+=+144+
OK