document.write( "Question 557023: thirty buliding operatives employed on a construction site work a 37 hour week. if the 30 operatives comprise tradesmen earning Ł4.75/ hour and labourers earning Ł4.25/ hour, how many tradesmen and how many labourers are there if the weekly bill is Ł5124.50. using matrices? \n" ); document.write( "

Algebra.Com's Answer #362506 by KMST(5328) $\"\"$ $\"About$

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Let $\"x\"$ be the number of tradesmen and $\"y\"$ be the number of laborers.
\n" ); document.write( " $\"x%2By=30\"$ and
\n" ); document.write( " $\"4.75x%2B4.25y=5124.50%2F37=138.50\"$ ---> $\"19x%2B17y=554\"$ (multiplying both sides times 4 to get rid of decimals)
\n" ); document.write( " $\"%28matrix%282%2C2%2C1%2C1%2C19%2C17%29%29\"$ $\"%28matrix%282%2C1%2Cx%2Cy%29%29\"$ = $\"%28matrix%282%2C1%2C30%2C554%29%29\"$
\n" ); document.write( "Now you have your matrices:
\n" ); document.write( " $\"A\"$ = $\"%28matrix%282%2C2%2C1%2C1%2C19%2C17%29%29\"$
\n" ); document.write( " $\"X\"$ = $\"%28matrix%282%2C1%2Cx%2Cy%29%29\"$ , and
\n" ); document.write( " $\"B\"$ = $\"%28matrix%282%2C1%2C30%2C554%29%29\"$
\n" ); document.write( "The equation with matrices is
\n" ); document.write( " $\"AX=B\"$
\n" ); document.write( "Now you have to find the inverse matrix $\"A%5E-1\"$ and calculate
\n" ); document.write( " $\"X\"$ = $\"A%5E-1B\"$
\n" ); document.write( "Whichever way you were taught to calculate it
\n" ); document.write( " $\"A%5E-1\"$ = $\"%28matrix%282%2C2%2C-17%2F2%2C1%2F2%2C19%2F2%2C-1%29%29\"$ and
\n" ); document.write( " $\"X\"$ = $\"%28matrix%282%2C2%2C-17%2F2%2C1%2F2%2C19%2F2%2C-1%29%29\"$ $\"%28matrix%282%2C1%2C30%2C554%29%29\"$ = $\"%28matrix%282%2C1%2C22%2C8%29%29\"$
\n" ); document.write( " $\"X\"$ = $\"%28matrix%282%2C1%2Cx%2Cy%29%29\"$ = $\"%28matrix%282%2C1%2C22%2C8%29%29\"$
\n" ); document.write( "So the number of tradesmen is $\"x=22\"$ , and
\n" ); document.write( "the number of laborers is $\"y=8\"$ . \n" ); document.write( "

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