SOLUTION: Juan wants to make a trail mix that contains 40% pecans. He has a bag of trail mix that has only 25% pecans at home and another bag that contains only pecans. How much of each shou

Algebra ->  Customizable Word Problem Solvers  -> Mixtures -> SOLUTION: Juan wants to make a trail mix that contains 40% pecans. He has a bag of trail mix that has only 25% pecans at home and another bag that contains only pecans. How much of each shou      Log On

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Question 862888: Juan wants to make a trail mix that contains 40% pecans. He has a bag of trail mix that has only 25% pecans at home and another bag that contains only pecans. How much of each should he mix together to make a 16-oz bag of trail mix that contains 40% pecans?
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let +a+ = ounces of 25% pecan mix needed
Let +b+ = ounces from bag of only pecans needed
+.25a+ = ounces of pecans in the 25% mix
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(1) +a+%2B+b+=+16+
(2) +%28+.25a+%2B+b+%29+%2F+16+=+.4+
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(2) +.25a+%2B+b+=+.4%2A16+
(2) +.25a+%2B+b+=+6.4+
(2) +25a+%2B+100b+=+640+
Multiply both sides of (1) by +25+
and subtract (1) from (2)
(2) +25a+%2B+100b+=+640+
(1) +-25a+-+25b+=+-400+
+75b+=+240+
+b+=+3.2+
and
(1) +a+%2B+3.2+=+16+
(1) +a+=+12.8+
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12.8 ounces of 25% pecan mix are needed
3.2 ounces from bag of only pecans are needed
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check:
(2) +%28+.25a+%2B+b+%29+%2F+16+=+.4+
(2) +%28+.25%2A12.8+%2B+3.2+%29+%2F+16+=+.4+
(2) +%28+3.2+%2B+3.2+%29+%2F+16+=+.4+
(2) +6.4+=+.4%2A16+
(2) +6.4+=+6.4+
OK