document.write( "Question 346645: Write a system of two equations using x and y to represent the following problem. A chemist is mixing two solutions together.
\n" ); document.write( "The chemist wants 100 gallons when complete. He is mixing a 24% solution with a 50% solution to get a 36% solution. How many gallons of each will he use?
\n" ); document.write( " \n" ); document.write( "

Algebra.Com's Answer #247851 by Fombitz(32388) $\"\"$ $\"About$

You can put this solution on YOUR website!

\n" ); document.write( "Let $\"x\"$ be the amount of 24% solution.
\n" ); document.write( "Let $\"y\"$ be the amount of 50% solution.
\n" ); document.write( "Volume equation:
\n" ); document.write( "1. $\"x%2By=100\"$
\n" ); document.write( "Concentration equation:
\n" ); document.write( " $\"24x%2B50y=36%28x%2By%29=36%28100%29=3600\"$
\n" ); document.write( "2. $\"12x%2B25y=1800\"$
\n" ); document.write( "From eq. 1,
\n" ); document.write( " $\"x=100-y\"$
\n" ); document.write( "Substitute into eq. 2,
\n" ); document.write( " $\"12%28100-y%29%2B25y=1800\"$
\n" ); document.write( " $\"1200-12y%2B25y=1800\"$
\n" ); document.write( " $\"13y=600\"$
\n" ); document.write( " $\"highlight%28y=600%2F13%29\"$ gallons
\n" ); document.write( "Then from eq. 1,
\n" ); document.write( " $\"x%2B600%2F13=100\"$
\n" ); document.write( " $\"x=1300%2F13-600%2F13\"$
\n" ); document.write( " $\"highlight%28x=700%2F13%29\"$ gallons
\n" ); document.write( " \n" ); document.write( "

\n" );