document.write( "Question 161181: Twice the larger number is 3 more than five times the smaller number. The sum of the 2 numbers is 4 times the larger number. What are the two numbers? \n" ); document.write( "

Algebra.Com's Answer #118734 by schrammbledeggs(41) $\"\"$ $\"About$

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Let x = larger number
\n" ); document.write( "Let y = smaller number\r
\n" ); document.write( "\n" ); document.write( "2x = 3 + 5y (first sentence transformed into an equation)
\n" ); document.write( "x + y = 4x (second sentence transformed into an equation)\r
\n" ); document.write( "\n" ); document.write( "Let's solve for y first by rearranging the 2nd equation into:\r
\n" ); document.write( "\n" ); document.write( "x + y - x = 4x - x
\n" ); document.write( "y = 3x\r
\n" ); document.write( "\n" ); document.write( "Substitute that value of y into the first equation:\r
\n" ); document.write( "\n" ); document.write( "2x = 3 + 5(3x)
\n" ); document.write( "2x = 3 + 15x
\n" ); document.write( "2x - 15x = 3 + 15x - 15x
\n" ); document.write( "-13x = 3
\n" ); document.write( "x = -3/13\r
\n" ); document.write( "\n" ); document.write( "Plug that back into the 2nd equation we got earlier...\r
\n" ); document.write( "\n" ); document.write( "y = 3x
\n" ); document.write( "y = 3(-3/13)
\n" ); document.write( "y = -9/13\r
\n" ); document.write( "\n" ); document.write( "So the larger number = -3/13 and the smaller number = -9/13 \n" ); document.write( "

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