document.write( "Question 333436: A mother is 8 times as old as her daughter and 4 times as old as her son. How old is each if the son is 4 years older than the daughter? \n" ); document.write( "

Algebra.Com's Answer #238935 by josmiceli(19441) $\"\"$ $\"About$

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Let $\"m\"$ = Mother's age
\n" ); document.write( "Let $\"d\"$ = Daughter's age
\n" ); document.write( "Let $\"s\"$ = Son's age
\n" ); document.write( "given:
\n" ); document.write( " $\"m+=+8d\"$
\n" ); document.write( " $\"m+=+4s\"$
\n" ); document.write( " $\"s+=+d+%2B+4\"$
\n" ); document.write( "This is 3 equations and 3 unknowns, so it's solvable
\n" ); document.write( "By substitution:
\n" ); document.write( " $\"m+=+4%2A%28d+%2B+4%29\"$
\n" ); document.write( " $\"m+=+4d+%2B+16\"$
\n" ); document.write( "Again, by substitution:
\n" ); document.write( " $\"8d+=+4d+%2B+16\"$
\n" ); document.write( " $\"4d+=+16\"$
\n" ); document.write( " $\"d+=+4\"$
\n" ); document.write( "and, since,
\n" ); document.write( " $\"m+=+8d\"$
\n" ); document.write( " $\"m+=+8%2A4\"$
\n" ); document.write( " $\"m+=+32\"$
\n" ); document.write( "also,
\n" ); document.write( " $\"s+=+d+%2B+4\"$
\n" ); document.write( " $\"s+=+4+%2B+4\"$
\n" ); document.write( " $\"s+=+8\"$
\n" ); document.write( "The Mother is 32, the Daughter is 4, and the Son is 8 \n" ); document.write( "

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