document.write( "Question 238610: Tim is one-third the age of Jenny. Ellen is one-half the age of Jenny. The sum of their ages is 44, How old is Tim? \n" ); document.write( "

Algebra.Com's Answer #175309 by josmiceli(19441) $\"\"$ $\"About$

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Let $\"t\"$ = Tim's age
\n" ); document.write( "Let $\"j\"$ = Jenny's age
\n" ); document.write( "Let $\"e\"$ = Ellen's age
\n" ); document.write( "given:
\n" ); document.write( " $\"t+=+%281%2F3%29%2Aj\"$
\n" ); document.write( " $\"e+=+%281%2F2%29%2Aj\"$
\n" ); document.write( " $\"t+%2B+j+%2B+e+=+44\"$
\n" ); document.write( "By substitution,
\n" ); document.write( " $\"%281%2F3%29%2Aj+%2B+j+%2B+%281%2F2%29%2Aj+=+44\"$
\n" ); document.write( "Multiply both sides by $\"6\"$
\n" ); document.write( " $\"2j+%2B+6j+%2B+3j+=+6%2A44\"$
\n" ); document.write( " $\"11j+=+264\"$
\n" ); document.write( " $\"j+=+24\"$
\n" ); document.write( "and, since
\n" ); document.write( " $\"t+=+%281%2F3%29%2Aj\"$
\n" ); document.write( " $\"t+=+%281%2F3%29%2A24\"$
\n" ); document.write( " $\"t+=+8\"$
\n" ); document.write( "Tim is 8 years old
\n" ); document.write( "check:
\n" ); document.write( " $\"e+=+%281%2F2%29%2Aj\"$
\n" ); document.write( " $\"e+=+%281%2F2%29%2A24\"$
\n" ); document.write( " $\"e+=+12\"$
\n" ); document.write( "and
\n" ); document.write( " $\"t+%2B+j+%2B+e+=+44\"$
\n" ); document.write( " $\"8+%2B+24+%2B+12+=+44\"$
\n" ); document.write( " $\"44+=+44\"$
\n" ); document.write( "OK \n" ); document.write( "

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