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

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Question 527745: 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!
He ends up with
+.4%2A16+=+6.4+ ounces of pecans
Let +a+ = ounces of 25% mix needed
Let +b+ = ounces of 100% mix needed
given:
(1) +a+%2B+b+=+16+
(2) +.25a+%2B+b+=+6.4+
Multiply both sides of (2) by
+100+. Then 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, since
(1) +a+%2B+b+=+16+
(1) +a+=+12.8+
12.8 ounces of 25% mix are needed
3.2 ounces of 100% mix are needed