SOLUTION: Craig is new at Bleachy Clean Cleaning Services. He needs to make 12 gallons of cleaner with a 15% concentration of bleach. He only has cleaners with 10% and 30% solutions. How man

Algebra ->  Coordinate Systems and Linear Equations  -> Linear Equations and Systems Word Problems -> SOLUTION: Craig is new at Bleachy Clean Cleaning Services. He needs to make 12 gallons of cleaner with a 15% concentration of bleach. He only has cleaners with 10% and 30% solutions. How man      Log On


   



Question 1059299: Craig is new at Bleachy Clean Cleaning Services. He needs to make 12 gallons of cleaner with a 15% concentration of bleach. He only has cleaners with 10% and 30% solutions. How many gallons of the 10% solution will he need?
Found 2 solutions by josgarithmetic, josmiceli:
Answer by josgarithmetic(39620) About Me  (Show Source):
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let +x+ = gallons of 10% solution needed
+12+-+x+ = gallons of 30% solution needed
+.1x+ = gallons of pure bleach in 10% solution
+.3%2A%28+12+-+x+%29+ = gallons of pure bleach in 30% solution
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+%28%28+.1x+%2B+.3%2A%28+12+-+x+%29+%29%29+%2F+12+=+.15+
+%28%28+.1x+%2B+3.6+-+.3x+%29%29+%2F+12+=+.15+
+%28%28+3.6+-+.2x+%29%29+%2F+12+=+.15+
+3.6+-+.2x+=+.15%2A12+
+3.6+-+.2x+=+1.8+
+.2x+=+1.8+
+x+=+9+
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9 gallons of 10% solution are needed
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check:
+%28%28+.1%2A9+%2B+.3%2A%28+12+-+9+%29+%29%29+%2F+12+=+.15+
+%28+%28+.9+%2B+.3%2A3+%29%29+%2F+12+=+.15+
+%28+.9+%2B+.9+%29+%2F+12+=+.15+
+1.8%2F12+=+.15+
+1.8+=+.15%2A12+
+1.8+=+1.8+
OK