document.write( "Question 1204237: Two mechanics worked on a car. The first mechanic charged 105 per hour, and the second mechanic charged 85 per hour. The mechanics worked for a combined total of 20 hours, and together they charged a total of 1800. How long did each mechanic work?\r
\n" ); document.write( "\n" ); document.write( " \n" ); document.write( "
Algebra.Com's Answer #840366 by greenestamps(13215)\"\" \"About 
You can put this solution on YOUR website!


\n" ); document.write( "The two responses you have received show basically the same solution, using two equations with two unknowns solved using substitution.

\n" ); document.write( "The other standard algebraic way of solving a system of two equations in two unknowns is elimination.

\n" ); document.write( "Let x be the number of hours worked at $85 per hour and y be the number of hours worked at $105 per hour. Then

\n" ); document.write( "the total time was 20 hours: \"x%2By=20\"
\n" ); document.write( "the total charge was $1800: \"85x%2B105y=1800\"

\n" ); document.write( "Simplify the second equation by dividing by the greatest common factor, 5.

\n" ); document.write( "\"17x%2B21y=360\"

\n" ); document.write( "Multiply the first equation by 17:

\n" ); document.write( "\"17x%2B17y=340\"

\n" ); document.write( "Eliminate x by subtracting one equation from the other.

\n" ); document.write( "\"4y=20\"
\n" ); document.write( "\"y=5\"

\n" ); document.write( "Use y=5 in the first equation \"x%2By=20\" to find x=15.

\n" ); document.write( "ANSWER: The mechanic who charges $85 per hour worked 15 hours on the car; the mechanic who charged $105 per hour worked 5 hours.

\n" ); document.write( "------------------------------------------------------------------------

\n" ); document.write( "Here is a quick and easy informal solution that uses exactly the same calculations as the formal elimination method above.

\n" ); document.write( "If all 20 hours were by the mechanic who charged $85 per hour, the total charge would be $1700. The actual charge was $100 more than that. Since the second mechanic charged $20 more per hour than the first, the number of hours he worked was $100/$20 = 5; so the first mechanic worked 15 hours.

\n" ); document.write( "-------------------------------------------------------------------------

\n" ); document.write( "And here is another, very different, informal way of solving any 2-part \"mixture\" problem like this.

\n" ); document.write( "The average charge per hour was $1800/20 = $90. Use a number line if it helps to observe/calculate that $90 is one-fourth of the way from $85 to $105. That means the mechanic who charged $105 per hour worked one-fourth of the total of 20 hours -- i.e., 5 hours; meaning the other mechanic worked 15 hours.

\n" ); document.write( " \n" ); document.write( "
\n" );