SOLUTION: emily is employed by sunset foods. she was instructed to create 30 pund mixture of peanuts that sell for 3.25 per pound and pecans that sell for 5.75 per pound. this mixture is to

Algebra ->  Customizable Word Problem Solvers  -> Age -> SOLUTION: emily is employed by sunset foods. she was instructed to create 30 pund mixture of peanuts that sell for 3.25 per pound and pecans that sell for 5.75 per pound. this mixture is to       Log On

Ad: Over 600 Algebra Word Problems at edhelper.com


   



Question 557001: emily is employed by sunset foods. she was instructed to create 30 pund mixture of peanuts that sell for 3.25 per pound and pecans that sell for 5.75 per pound. this mixture is to be worth 4.75 per pound. how many pounds of peanuts and pecans must be used?
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let a = pounds of peanuts needed
Let b = pounds of pecans needed
given:
(1) +a+%2B+b+=+30+ pounds
(2) +%28+3.25a+%2B+5.75b+%29+%2F+30+=+4.75+
-------------------------------
(2) +3.25a+%2B+5.75b+=+4.75%2A30+
(2) +3.25a+%2B+5.75b+=+142.5+
(2) +325a+%2B+575b+=+14250+
(2) +13a+%2B+23b+=+570+
Multiply both sides of (1) by +13+
and subtract (1) from (2)
(2) +13a+%2B+23b+=+570+
(1) +-13a+-+13b+=+-390+
+10b+=+180+
+b+=+18+
and, since
(1) +a+%2B+b+=+30+
(1) +a+%2B+18+=+30+
(1) +a+=+12+
12 pounds of peanuts are needed
18 pounds of pecans are needed
check answer:
(2) +%28+3.25%2A12+%2B+5.75%2A18+%29+%2F+30+=+4.75+
(2) +%28+39+%2B+103.5+%29+%2F+30+=+4.75+
(2) +142.5+%2F+30+=+4.75+
(2) +142.5+=+142.5+
OK