SOLUTION: Mary needs 180 pounds of a 9 % nut mixture. She has a container of 33 % pecans and a container of 1 % cashews. How many pounds of cashews should she mix to get the 9% mixture?

Algebra ->  Customizable Word Problem Solvers  -> Mixtures -> SOLUTION: Mary needs 180 pounds of a 9 % nut mixture. She has a container of 33 % pecans and a container of 1 % cashews. How many pounds of cashews should she mix to get the 9% mixture?      Log On

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Question 814273: Mary needs 180 pounds of a 9 % nut mixture. She has a container of 33 % pecans and a container of 1 % cashews. How many pounds of cashews should she mix to get the 9% mixture?
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
It took me a few minutes to realize that
a pecan is not a nut. It's a seed right?
Let +a+ = pounds of pecan mixture needed
Let +b+ = pounds of cashew mixture needed
---------------
(1) +a+%2B+b+=+180+
(2) +%28+.33a+%2B+.01b+%29+%2F+180+=+.09+
----------------------------
(2) +.33a+%2B+.01b+=+.09%2A180+
(2) +.33a+%2B+.01b+=+16.2+
(2) +33a+%2B+b+=+1620+
and
(1) +b+=+180+-+a+
Substitute (1) into (2)
(2) +33a+%2B+180+-+a+=+1620+
(2) +32a+=+1440+
(2) +a+=+45+
and, since
(1) +b+=+180+-+a+
(1) +b+=+180+-+45+
(1) +b+=+135+
135 pounds of cashew mixture are needed, and
the actual pounds of cashews are:
+.01%2A135+ = 1.35 pounds
check:
(2) +%28+.33a+%2B+.01b+%29+%2F+180+=+.09+
(2) +%28+.33%2A45+%2B+.01%2A135+%29+%2F+180+=+.09+
(2) +%28+14.85+%2B+1.35+%29+%2F+180+=+.09+
(2) +16.2+=+.09%2A180+
(2) +16.2+=+16.2+
OK