SOLUTION: An engine has a 6.2 litre capacity cooling system. If the most ideal solution of antifreeze for this engine is a 57.6 % solution (a mix of 57.6 % pure antifreeze and 42.4 % water).

Algebra ->  Human-and-algebraic-language -> SOLUTION: An engine has a 6.2 litre capacity cooling system. If the most ideal solution of antifreeze for this engine is a 57.6 % solution (a mix of 57.6 % pure antifreeze and 42.4 % water).      Log On


   



Question 1020888: An engine has a 6.2 litre capacity cooling system. If the most ideal solution of antifreeze for this engine is a 57.6 % solution (a mix of 57.6 % pure antifreeze and 42.4 % water). How much pure antifreeze (in litres) must be combined with a 40.4 % solution to achieve 6.2 litres of the ideal solution?
Express your answer to three significant digits.

Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let +x+ = liters of pure antifreeze to be added
+6.2+-+x+ = liters of 40.4% solution to use
+.404%2A%28+6.2+-+x+%29+ = liters of pure antifreeze in 40.4% solution
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I can say:
+%28+x+%2B+.404%2A%28+6.2+-+x+%29+%29+%2F+6.2+=+.576+
+%28+x+%2B+2.5048+-+.404x+%29+%2F+6.2+=+.576+
+.596x+%2B+2.5048+=+.576%2A6.2+
+.596x+=+3.5712+-+2.5048+
+.596x+=+1.0664+
+x+=+1.7893+
1.789 liters of pure antifreeze is needed
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check:
+%28+x+%2B+.404%2A%28+6.2+-+x+%29+%29+%2F+6.2+=+.576+
+%28+1.789+%2B+.404%2A%28+6.2+-+1.789+%29+%29+%2F+6.2+=+.576+
+%28+1.789+%2B+.404%2A4.4107+%29+%2F+6.2+=+.576+
+%28+1.789+%2B+1.7819+%29+%2F+6.2+=+.576+
+3.571+=+.576%2A6.2+
+3.571+=+3.571+
OK
Hope I got it!