SOLUTION: Vietnamese cinnamon costs $18 for a pound, and Indonesian cinnamon costs $30 for a pound. Penzey's wants to create a 12 lb mixture of cinnamon that costs $25/lb. How much of each t

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Question 899324: Vietnamese cinnamon costs $18 for a pound, and Indonesian cinnamon costs $30 for a pound. Penzey's wants to create a 12 lb mixture of cinnamon that costs $25/lb. How much of each type should they mix together?
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let +a+= pounds of v.c. needed
Let +b+ = pounds of i.c. needed
-------------------------------
(1) +a+%2B+b+=+12+
(2) +%28+18a+%2B+30b+%29+%2F+12+=+25+
------------------------------
(2) +18a+%2B+30b+=+300+
(2) +6a+%2B+10b+=+100+
(2) +3a+%2B+5b+=+50+
----------------------
Multiply both sides of (1) by +3+
and subtract (1) from (2)
(2) +3a+%2B+5b+=+50+
(1) +-3a+-3b+=+-36+
---------------------
+2b+=+14+
+b+=+7+
and, since
(1) +a+%2B+b+=+12+
(1) +a+=+5+
---------------
5 pounds of v.c. are needed
7 pounds of i.c. are needed
-------------------------
check:
(2) +%28+18%2A5+%2B+30%2A7+%29+%2F+12+=+25+
(2) +%28+90+%2B+210+%29+%2F+12+=+25+
(2) +300+%2F+12+=+25+
(2) +300+=+300+
OK