SOLUTION: How many ounces of a 35% alcohol solution must be mixed with 9 ounces of a 40% alcohol solution to make a 36% alcohol​ solution? The amount of 35 % alcohol solution is how

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Question 1069967: How many ounces of a 35% alcohol solution must be mixed with 9 ounces of a 40% alcohol solution to make a 36% alcohol​ solution?
The amount of 35 % alcohol solution is how many ounces?
​(Type an integer or a​ decimal.)
A cook needs to mix a regular ranch dressing containing 47​% fat with a light ranch dressing containing 37​% fat to result in 7 cups of a dressing containing 42​% fat. How many cups of each kind of dressing should be​ mixed?
The mixture should contain
how many cups of regular dressing and
how many cups of light dressing.

Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
(1)
Let +x+ = ounces of the 35% alcohol solution needed
+.35x+ = ounces of alcohol in the 35% solution
+.4%2A9+=+3.6+ = ounces of alcohol in the 40% solution
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+%28+.35x+%2B+3.6+%29+%2F+%28+x+%2B+9+%29+=+.36+
+.35x+%2B+3.6+=+.36%2A%28+x+%2B+9+%29+
+.35x+%2B+3.6+=+.36x+%2B+3.24+
+.01x+=+3.6+-+3.24+
+.01x+=+.36+
+x+=+36+
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36 ounces of the 35% alcohol solution are needed
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check:
+%28+.35x+%2B+3.6+%29+%2F+%28+x+%2B+9+%29+=+.36+
+%28+.35%2A36+%2B+3.6+%29+%2F+%28+36+%2B+9+%29+=+.36+
+%28+12.6+%2B+3.6+%29+%2F+45+=+.36+
+16.2+%2F+45+=+.36+
+16.2+=+16.2+
OK