document.write( "Question 362574: The smaller of two numbers is 3 less than twice the larger number. If the larger number is decreased by 10, the result is the same as the smaller number. Find the numbers. \n" ); document.write( "

Algebra.Com's Answer #258426 by josmiceli(19441) $\"\"$ $\"About$

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Call the smaller number $\"a\"$
\n" ); document.write( "Call the larger number $\"b\"$
\n" ); document.write( "given:
\n" ); document.write( " $\"a+=+2b+-+3\"$
\n" ); document.write( " $\"b+-+10+=+a\"$
\n" ); document.write( "Substitute $\"a\"$ in the 1st equation into the 2nd equation
\n" ); document.write( " $\"b+-+10+=+2b+-+3\"$
\n" ); document.write( " $\"b+=+-7\"$
\n" ); document.write( "and, since
\n" ); document.write( " $\"a+=+2b+-+3\"$
\n" ); document.write( " $\"a+=+-14+-+3\"$
\n" ); document.write( " $\"a+=+-17\"$
\n" ); document.write( "The smaller number is $\"-17\"$
\n" ); document.write( "The larger number is $\"-7\"$
\n" ); document.write( "check:
\n" ); document.write( " $\"a+=+2b+-+3\"$
\n" ); document.write( " $\"-17+=+2%2A%28-7%29+-+3\"$
\n" ); document.write( " $\"-17+=+-17\"$
\n" ); document.write( "OK, and
\n" ); document.write( " $\"b+-+10+=+a\"$
\n" ); document.write( " $\"-7+-+10+=+-17\"$
\n" ); document.write( " $\"-17+=+-17\"$
\n" ); document.write( "OK \n" ); document.write( "

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