document.write( "Question 620642: the difference of two numbers is 47. The first number is 31 less than twice the second number. What are the two numbers? \n" ); document.write( "

Algebra.Com's Answer #390344 by dragonwalker(73) $\"\"$ $\"About$

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So let us call the first number 'n'. We know that the second number is n+47 or n-47\r
\n" ); document.write( "\n" ); document.write( "So the first number, n = 2(n + 47)-31 or 2(n - 47)-31\r
\n" ); document.write( "\n" ); document.write( "solve for n when n is smaller than the second number (i.e. second number is equal to n+47):\r
\n" ); document.write( "\n" ); document.write( "n = 2(n+47)-31
\n" ); document.write( "n = 2n+94-31
\n" ); document.write( "n-2n=94-31
\n" ); document.write( "-n=63
\n" ); document.write( "n=-63\r
\n" ); document.write( "\n" ); document.write( "and the second number is n+47 = -16\r
\n" ); document.write( "\n" ); document.write( "when n is the larger number and therefore the second number is smaller (n-47):\r
\n" ); document.write( "\n" ); document.write( "n = 2(n-47)-31
\n" ); document.write( "n = 2n-94-31
\n" ); document.write( "n-2n = -125
\n" ); document.write( "-n = -125
\n" ); document.write( "n=125\r
\n" ); document.write( "\n" ); document.write( "and the second number is n-47 = 78\r
\n" ); document.write( "\n" ); document.write( "If the question definitely means that the first number is the smaller one then you would just use the n+47 and end up with the two negative numbers -63 and -16\r
\n" ); document.write( "\n" ); document.write( "If it does not imply then you would have to give both solutions but I actually expect that the first scenario is expected.\r
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