document.write( "Question 175389: One number is 16 more than the other. If the smaller number is subtracted from two thirds of the larger, the result is one fourth of the sum of the two numbers. Find the numbers. \n" ); document.write( "

Algebra.Com's Answer #130442 by josmiceli(19441) $\"\"$ $\"About$

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Call the larger number $\"a\"$
\n" ); document.write( "Call the smaller number $\"b\"$
\n" ); document.write( "Given:
\n" ); document.write( "(1) $\"a+=+b+%2B+16\"$
\n" ); document.write( "(2) $\"%282%2F3%29%2Aa+-+b+=+%281%2F4%29%28a+%2B+b%29\"$
\n" ); document.write( "multiply both sides by $\"12\"$
\n" ); document.write( " $\"8a+-+12b+=+3a+%2B+3b\"$
\n" ); document.write( " $\"5a+=+15b\"$
\n" ); document.write( " $\"a+=+3b\"$
\n" ); document.write( "Substitute this value for $\"a\"$ in (1)
\n" ); document.write( " $\"3b+=+b+%2B+16\"$
\n" ); document.write( " $\"2b+=+16\"$
\n" ); document.write( " $\"b+=+8\"$
\n" ); document.write( "and
\n" ); document.write( " $\"a+=+3b\"$
\n" ); document.write( " $\"a+=+24\"$
\n" ); document.write( "Yhe numbers are 24 and 8
\n" ); document.write( "check:
\n" ); document.write( "(2) $\"%282%2F3%29%2Aa+-+b+=+%281%2F4%29%28a+%2B+b%29\"$
\n" ); document.write( " $\"%282%2F3%29%2A24+-+8+=+%281%2F4%29%2824+%2B+8%29\"$
\n" ); document.write( " $\"16+-+8+=+%281%2F4%29%2A32\"$
\n" ); document.write( " $\"8+=+8\"$
\n" ); document.write( "OK \n" ); document.write( "

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