SOLUTION: Making snacks with candy and cereal,how many pounds of candy at $6 per pound would be required to be mixed with cereal costing $8 a pound to create a 10 pound mixture costing $7.5

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Question 708400: Making snacks with candy and cereal,how many pounds of candy at $6 per pound would be required to be mixed with cereal costing $8 a pound to create a 10 pound mixture costing $7.50 per pound.
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let +a+ = pounds of candy at $6 per pound needed
Let +b+ = pounds of candy at $8 per pound needed
given:
(1) ++6a+%2B+8b+=+10%2A7.5+
(2) +a+%2B+b+=+10+
-----------------
(1) +6a+%2B+8b+=+75+
Multiply both sides of (2) by +6+
and subtract (2) from (1)
(1) +6a+%2B+8b+=+75+
(2) +-6a+-+6b+=+-60+
+2b+=+15+
+b+=+7.5+
and, since
(2) +a+%2B+b+=+10+
(2) +a+=+2.5+
2.5 pounds of candy at $6/pound are needed
7.5 pounds of candy at $8/pound are needed
check:
(1) +6%2A2.5+%2B+8%2A7.5+=+75+
(1) +15+%2B+60+=+75+
(1) +75+=+75+
OK