document.write( "Question 474228: The sum of a man's age and his grandmother's age is 102. Eighteen years age his grandmother was 10 times as old as he was then. Find their present ages. \n" ); document.write( "

Algebra.Com's Answer #325279 by josmiceli(19441) $\"\"$ $\"About$

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Let $\"a\"$ = Man's present age
\n" ); document.write( "Let $\"b\"$ = Grandmother's present age
\n" ); document.write( " $\"+a+-+18+\"$ = Man's age 18 years ago
\n" ); document.write( " $\"+b+-+18+\"$ = Gradmother's age 18 years ago
\n" ); document.write( "given:
\n" ); document.write( "(1) $\"+a+%2B+b+=+102+\"$
\n" ); document.write( "(2) $\"+b+-+18+=+10%2A%28a+-+18%29+\"$
\n" ); document.write( "------------------------
\n" ); document.write( "(2) $\"+b+-+18+=+10a+-+180+\"$
\n" ); document.write( "(2) $\"+10a+-+b+=+180+-+18+\"$
\n" ); document.write( "(2) $\"+10a+-+b+=+162+\"$
\n" ); document.write( "Add (2) to (1)
\n" ); document.write( "(2) $\"+10a+-+b+=+162+\"$
\n" ); document.write( "(1) $\"+a+%2B+b+=+102+\"$
\n" ); document.write( " $\"+11a+=+264+\"$
\n" ); document.write( " $\"+a+=+24+\"$
\n" ); document.write( "And, from (1),
\n" ); document.write( " $\"+a+%2B+b+=+102+\"$
\n" ); document.write( " $\"+24+%2B+b+=+102+\"$
\n" ); document.write( " $\"+b+=+78+\"$
\n" ); document.write( "The man is 24 and the Grandmother is 78
\n" ); document.write( "-------------
\n" ); document.write( "check:
\n" ); document.write( "(2) $\"+b+-+18+=+10%2A%28a+-+18%29+\"$
\n" ); document.write( "(2) $\"+78+-+18+=+10%2A%2824+-+18%29+\"$
\n" ); document.write( "(2) $\"+60+=+60+\"$
\n" ); document.write( "OK \n" ); document.write( "

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