document.write( "Question 1100983: The sum of two numbers is 47. The sum of the smaller and 2 times the larger is 76 . Find the numbers? \n" ); document.write( "

Algebra.Com's Answer #715542 by greenestamps(13200) $\"\"$ $\"About$

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\n" ); document.write( "You can solve this without algebra, by using logical reasoning.

\n" ); document.write( "The first sum is the sum of each of the two numbers once; the second sum is different only in that the second number is added twice.

\n" ); document.write( "So the difference between the two sums is the second number.

\n" ); document.write( "76-47 = 29, so the second number is 29.

\n" ); document.write( "Then the first number is 47-29 = 18.

\n" ); document.write( "The algebraic solution does exactly the same thing as this informal solution. So you should learn the formal process for solving problems like this using algebra; but you should also try to get some exercise in logical reasoning by solving the problem without the formal methods.

\n" ); document.write( "Here is an algebraic solution:

\n" ); document.write( " $\"x%2By+=+47\"$
\n" ); document.write( " $\"x%2B2y+=+76\"$
\n" ); document.write( " $\"y+=+29\"$ (subtract the first equation from the second)
\n" ); document.write( " $\"x+=+47-29+=+18\"$

\n" ); document.write( "You can see that, in this case, the steps of the formal solution are exactly the same as the steps of the informal solution. \n" ); document.write( "

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