SOLUTION: A shop that sells nuts has one mixture that is 25% almonds and 75% cashews. A second mixture is 55% almonds and 45% cashews The manager wants to make a new mixture that is 43% alm

Algebra ->  Customizable Word Problem Solvers  -> Mixtures -> SOLUTION: A shop that sells nuts has one mixture that is 25% almonds and 75% cashews. A second mixture is 55% almonds and 45% cashews The manager wants to make a new mixture that is 43% alm      Log On

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Question 730921: A shop that sells nuts has one mixture that is 25% almonds and 75% cashews. A second mixture is 55% almonds and 45% cashews The manager wants to make a new mixture that is 43% almonds. She wants to use 37 ounces more of the second mixture than that of the first. How many ounces of each mixture must she use?
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let +a+ = ounces of the 1st mixture needed
Let +b+ = ounces of the 2nd mixture needed
+.25a+ = ounces of almonds in 1st mixture
+.55b+ = ounces of almonds in 2nd mixture
--------------
+b+=+a+%2B+37+
+%28+.25a+%2B+.55b+%29+%2F+%28+a+%2B+b+%29+=+.43+
+.25a+%2B+.55b+=+.43%2A%28+a+%2B+b+%29+
+.25a+%2B+.55b+=+.43a+%2B+.43b+%29+
By substitution:
+.25a+%2B+.55%2A%28+a+%2B+37+%29+=+.43a+%2B+.43%2A%28+a+%2B+37+%29+
+.25a+%2B+.55a+%2B+20.35+=+.43a+%2B+.43a+%2B+15.91+
+.8a+%2B+20.35+=+.86a+%2B+15.91+
+.06a+=+4.44+
+a+=+74+
and
+b+=+a+%2B+37+
+b+=+111+
74 ounces of the 1st mixture is needed
111 ounces of the 2nd mixture is needed
check:
+%28+.25a+%2B+.55b+%29+%2F+%28+a+%2B+b+%29+=+.43+
+%28+.25%2A74+%2B+.55%2A111+%29+%2F+%28+74+%2B+111+%29+=+.43+
+%28+18.5+%2B+61.05+%29+%2F+185+=+.43+
+79.55+=+.43%2A185+
+79.55+=+79.55+
OK