document.write( "Question 1035233: If two numbers total 107 5/6 and if three times the smaller number is 13 5/6 less than the larger number, what is the larger number? \n" ); document.write( "

Algebra.Com's Answer #649909 by Cromlix(4381) $\"\"$ $\"About$

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Hi there,
\n" ); document.write( "two numbers total 107 5/6
\n" ); document.write( "x + y = 107 5/6
\n" ); document.write( "x + y = 647/6.......(1)
\n" ); document.write( "three times the smaller number is 13 5/6 less than the larger number.
\n" ); document.write( "3x = y - 13 5/6
\n" ); document.write( "3x - y = - 83/6.....(2)
\n" ); document.write( "...............
\n" ); document.write( "x + y = 647/6.......(1)
\n" ); document.write( "3x - y = - 83/6.....(2)
\n" ); document.write( "Add Eq(1) + (2)
\n" ); document.write( "4x = 647/6 + (- 83/6)
\n" ); document.write( "4x = 647/6 - 83/6
\n" ); document.write( "4x = 564/6
\n" ); document.write( "x = 564/24
\n" ); document.write( "x = 47/2
\n" ); document.write( "Substitute x = 47/2 in
\n" ); document.write( "x + y = 647/6.......(1)
\n" ); document.write( "47/2 + y = 647/6
\n" ); document.write( "y = 647/6 - 47/2
\n" ); document.write( "y = (647 - 141)/6
\n" ); document.write( "y = 506/6.
\n" ); document.write( "y = 253/3
\n" ); document.write( "So x = 23 1/2
\n" ); document.write( "y = 84 1/3. (The larger number)
\n" ); document.write( "Proof:
\n" ); document.write( "x + y = 647/6
\n" ); document.write( "47/2 + 253/3 = (141 + 506)/6 = 647/6.
\n" ); document.write( "Hope this helps :-) \n" ); document.write( "

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