document.write( "Question 1145311: One mixture contains 20% sugar and 60% salt while another contains 50% sugar and 30% salt. How many cups of each mixture should you combine so that the result contains 8 cups of sugar and 6 cups of salt? \n" ); document.write( "

Algebra.Com's Answer #766531 by greenestamps(13200) $\"\"$ $\"About$

You can put this solution on YOUR website!

\n" ); document.write( "x = cups of the first mixture
\n" ); document.write( "y = cups of the second mixture

\n" ); document.write( "sugar equation: $\"0.2x%2B0.5y+=+8\"$
\n" ); document.write( "salt equation: $\"0.6x%2B0.3y+=+6\"$

\n" ); document.write( "Solve by elimination: multiply the first equation by 3 and subtract the second equation.

\r\n" );
document.write( "   0.6x + 1.5y = 24\r\n" );
document.write( "   0.6x + 0.3y =  6\r\n" );
document.write( "  ------------------\r\n" );
document.write( "          1.2y = 18

\n" ); document.write( "y = 18/1.2 = 15

\n" ); document.write( "Substitute y=15 in one of the original equations:

\n" ); document.write( " $\"0.2x%2B0.5%2815%29+=+8\"$
\n" ); document.write( " $\"0.2x%2B7.5+=+8\"$
\n" ); document.write( " $\"0.2x+=+0.5\"$
\n" ); document.write( " $\"x+=+0.5%2F0.2+=+2.5\"$

\n" ); document.write( "ANSWER: 2.5 cups of the first mixture and 15 cups of the second.

\n" ); document.write( "CHECK:
\n" ); document.write( "sugar: 0.2(2.5)+0.5(15) = 0.5+7.5 = 8
\n" ); document.write( "salt: 0.6(2.5)+0.3(15) = 1.5+4.5 = 6 \n" ); document.write( "

\n" );