document.write( "Question 733612: A mechanic has found that a car with a 16-quart radiator has 40% antifreeze mixture in the radiator. He has a 80% antifreeze solution. How much of the 40% solution would he have to replace with the 80% solution to get the radiator up to 55% antifreeze solution? (You must set up an equation and solve to receive credit) \n" ); document.write( "

Algebra.Com's Answer #448528 by KMST(5328) $\"\"$ $\"About$

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The radiator contains 16 quarts of solution that is too weak.
\n" ); document.write( "If the mechanic removes $\"x\"$ quarts of the 40% solution in the radiator, the radiator will have $\"16-x\"$ quarts of solution, containing
\n" ); document.write( " $\"%2816-x%29%2A0.4\"$ quarts of antifreeze.
\n" ); document.write( "After that, the mechanic adds $\"x\"$ quarts of 80% antifreeze solution, containing
\n" ); document.write( " $\"0.8%2Ax\"$ quarts of antifreeze.
\n" ); document.write( "At the end, the radiator will again contain 16 quarts of solution:
\n" ); document.write( " $\"16-x%2Bx=16\"$ , but the amount of antifreeze in the radiator will be
\n" ); document.write( " $\"%2816-x%29%2A0.4%2B0.8x\"$
\n" ); document.write( "For the solution to be 55% antifreeze, the amount of antifreeze in the radiator should be
\n" ); document.write( " $\"16%2A0.55\"$ quarts or $\"8.8\"$ quarts
\n" ); document.write( "The equation we should use to calculate the $\"x\"$ value needed is
\n" ); document.write( " $\"%2816-x%29%2A0.4%2B0.8x=16%2A0.55\"$ or $\"%2816-x%29%2A0.4%2B0.8x=8.8\"$
\n" ); document.write( " $\"%2816-x%29%2A0.4%2B0.8x=8.8\"$ --> $\"6.4-0.4x%2B0.8x=8.8\"$ --> $\"6.4%2B0.4x=8.8\"$ --> $\"0.4x=8.8-6.4\"$ --> $\"0.4x=2.4\"$ --> $\"x=2.4%2F0.4\"$ --> $\"highlight%28x=6%29\"$
\n" ); document.write( "The mechanic should remove 6 quarts of solution from the radiator and replace them with 6 quarts of 80% antifreeze solution. \n" ); document.write( "

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