document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1184557>Question 1184557</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Two mechanics worked on a car. The first mechanic charged $105 per hour, and the second mechanic charged $50 per hour. The mechanics worked for a combined total of 20 hours, and together they charged a total of $1825. How long did each mechanic work? </SPAN>\n" );
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document.write( "First a traditional algebraic setup for solving the problem....<br><BR>\n" );
document.write( "x = hours at $105 per hour<BR>\n" );
document.write( "20-x = hours at $50 per hour<br><BR>\n" );
document.write( "Total charge for 20 hours was $1825:<br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=105%28x%29%2B50%2820-x%29=1825 ALIGN=MIDDLE  ALT=\"105%28x%29%2B50%2820-x%29=1825\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "Solve using basic algebra.<br><BR>\n" );
document.write( "And a solution method without algebra, using logical reasoning and some mental arithmetic....<br><BR>\n" );
document.write( "All 20 hours at $105 per hour would cost $2100; all 20 hours at $50 per hour would cost $1000; the actual cost was $1825.<br><BR>\n" );
document.write( "Look at the three costs on a number line -- 1000, 1825, and 2100 -- and observe/calculate that 1825 is 825/1100 = 3/4 of the way from 1000 to 2100.<br><BR>\n" );
document.write( "That means 3/4 of the hours were at the higher rate.<br><BR>\n" );
document.write( "ANSWER: 3/4 of 20 hours, or 15 hours, at $105 per hour; the other 5 hours at $50 per hour<br><BR>\n" );
document.write( "CHECK: 15(105)+5(50)=1575+250=1825<br><BR>\n" );
document.write( " </SPAN>\n" );
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