document.write( "Question 167030: In an office building, a room contains 54 chairs. The number of chairs per row is three less than twice the number of rows. Find the number of rows and the number of chairs per row. \n" ); document.write( "

Algebra.Com's Answer #123100 by ptaylor(2198) $\"\"$ $\"About$

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Let x=number of rows
\n" ); document.write( "Let y=number of chairs per row
\n" ); document.write( "xy=54----------------------------------eq1
\n" ); document.write( "and
\n" ); document.write( "y+3=2x---------------------------------eq2
\n" ); document.write( "From eq1, we see that y=54/x. Substitute this into eq2:\r
\n" ); document.write( "\n" ); document.write( "54/x + 3=2x multiply each term by x
\n" ); document.write( "54+3x=2x^2 subtract 2x^2 from each side\r
\n" ); document.write( "\n" ); document.write( "-2x^2+3x+54=0 multiply each term by -1
\n" ); document.write( "2x^2-3x-54=0---------------------quadratic in standard form and it can be factored
\n" ); document.write( "(2x+9)(x-6)=0
\n" ); document.write( "x=6--------------------------number of rows
\n" ); document.write( "Forget the negative value for x. Rows are positive and besides we can't have fractions of rows
\n" ); document.write( "Substitute x=6 into eq1:
\n" ); document.write( "6y=54
\n" ); document.write( "y=9----------------------------number of chairs per row
\n" ); document.write( "CK
\n" ); document.write( "The number of chairs per row is three less than twice the number of rows.\r
\n" ); document.write( "\n" ); document.write( "9+3=2*6
\n" ); document.write( "12=12
\n" ); document.write( "also
\n" ); document.write( "6*9=54
\n" ); document.write( "54=54\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "Hope this helps---ptaylor\r
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