document.write( "Question 1016308: A student works two part-time jobs. He earns $9 an hour for working at the college library and $14 an hour for construction work. To save time for study, he limits his work to 25 hours a week. If he enjoys the work at the library more, how many hours can he work at the library and still earn at least $285 a week? \n" ); document.write( "

Algebra.Com's Answer #632720 by josgarithmetic(39616) $\"\"$ $\"About$

You can put this solution on YOUR website!

\r\n" );
document.write( "x   construction work hours\r\n" );
document.write( "y   library work hours\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "Account for wages\r\n" );
document.write( "9y+14x>=285\r\n" );
document.write( "\r\n" );
document.write( "Account for work time\r\n" );
document.write( "x+y<=25\r\n" );
document.write( "

\r
\n" ); document.write( "\n" ); document.write( "System of inequalities, $\"system%2814x%2B9y%3E=285%2Cx%2By%3C=25%29\"$ \r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "A possible method can be to graph the system $\"system%28y%3E=-%2814%2F9%29x%2B95%2F3%2Cy%3C=-x%2B25%2Cx%3E=0%2Cy%3E=0%29\"$ \r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "Here is a graph without filling any of the inequality regions:
\n" ); document.write( " $\"graph%28400%2C400%2C-2%2C30%2C-2%2C30%2C-%2814%2F9%29x%2B95%2F3%2C-x%2B25%29\"$ \r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "The most hours at the library is want is wanted, and in examining the graph, this will be at the intersection point of the two lines. That could be THE BEST answer.
\n" ); document.write( "-
\n" ); document.write( "You can do the algebra if you want, equating the two expressions for y, solve for x and y; and find x=12 for construction job hours, and y=13 for library work hours.
\n" ); document.write( " \n" ); document.write( "

\n" );