document.write( "Question 984881: My son my father and I were all born on fathers day. When my son was born I was 3/7 the age of my father. Today my son is the age I was when he was born; in four years he will be exactly 1/3 the age of my father. how old was I when my son was born? \n" ); document.write( "

Algebra.Com's Answer #605812 by josmiceli(19441) $\"\"$ $\"About$

You can put this solution on YOUR website!
If they were all born on the same day of the year,
\n" ); document.write( "then the differences in their ages are integers
\n" ); document.write( "( whole numbers )
\n" ); document.write( "--------------------
\n" ); document.write( "Let $\"+m+\"$ = my age now
\n" ); document.write( "Let $\"+s+\"$ = my son's age now
\n" ); document.write( "Let $\"+f+\"$ = my father's age now
\n" ); document.write( "-----------------------------
\n" ); document.write( "\"Today my son is the age I was when he was born\"
\n" ); document.write( "My age when my son was born is:
\n" ); document.write( " $\"+m+-+s+\"$
\n" ); document.write( "\"Today my son is the age I was\"
\n" ); document.write( " $\"+s+=+m+-+s+\"$
\n" ); document.write( " $\"+2s+=+m+\"$
\n" ); document.write( "(1) $\"+m+=+2s+\"$
\n" ); document.write( "-------------
\n" ); document.write( "\"In four years he will be exactly 1/3 the age of my father.\"
\n" ); document.write( "(2) $\"+s+%2B+4+=+%281%2F3%29%2A%28+f%2B4+%29+\"$
\n" ); document.write( "-------------------------
\n" ); document.write( "Also:
\n" ); document.write( "\"When my son was born I was 3/7 the age of my father.\"
\n" ); document.write( "As already shown, I was $\"+m+-+s+\"$ years old when my
\n" ); document.write( "son was born, so
\n" ); document.write( "(3) $\"+m+-+s+=+%283%2F7%29%2A%28+f+-+s+%29+\"$
\n" ); document.write( "( note that I have to subtract my son's age from
\n" ); document.write( "my father's age also )
\n" ); document.write( "-----------------------
\n" ); document.write( "(1), (2), and (3) are 3 equations with 3 unknowns,
\n" ); document.write( "so it's solvable
\n" ); document.write( "-----------------
\n" ); document.write( "(2) $\"+3%2A%28+s+%2B+4+%29+=+f+%2B+4+\"$
\n" ); document.write( "(2) $\"+3s+%2B+12+=+f+%2B+4+\"$
\n" ); document.write( "(2) $\"+f+=+3s+%2B+8+\"$
\n" ); document.write( "-------------------
\n" ); document.write( "(3) $\"+7%2A%28+m+-+s+%29+=+3%2A%28+f+-+s+%29+\"$
\n" ); document.write( "(3) $\"+7m+-+7s+=+3f+-+3s+\"$
\n" ); document.write( "(3) $\"+7m+-+4s+-+3f+=+0+\"$
\n" ); document.write( "------------------------
\n" ); document.write( "By substitution:
\n" ); document.write( "(3) $\"+7%2A2s+-+4s+-+3f+=+0+\"$
\n" ); document.write( "and
\n" ); document.write( "(3) $\"+7%2A2s+-+4s+-+3%2A%28+3s+%2B+8+%29+=+0+\"$
\n" ); document.write( "(3) $\"+14s+-+4s+-+9s+-+24+=+0+\"$
\n" ); document.write( "(3) $\"+s+=+24+\"$
\n" ); document.write( "----------------
\n" ); document.write( "(2) $\"+f+=+3%2A24+%2B+8+\"$
\n" ); document.write( "(2) $\"+f+=+72+%2B+8+\"$
\n" ); document.write( "(2) $\"+f+=+80+\"$
\n" ); document.write( "----------------
\n" ); document.write( "(3) $\"+7m+-+4%2A24+-+3%2A80+=+0+\"$
\n" ); document.write( "(3) $\"+7m+-+96+-+240+=+0+\"$
\n" ); document.write( "(3) $\"+7m+=+336+\"$
\n" ); document.write( "(3) $\"+m+=+48+\"$
\n" ); document.write( "-----------------
\n" ); document.write( "I was $\"+m+-+s+\"$ when my son was born
\n" ); document.write( " $\"+m+-+s+=+48+-+24+\"$
\n" ); document.write( " $\"+m+-+s+=+24+\"$
\n" ); document.write( "I was 24 yrs old when my son was born
\n" ); document.write( "-------------------
\n" ); document.write( "check:
\n" ); document.write( "When my son was born I was 3/7 the age of my father.
\n" ); document.write( " $\"+24+=+%283%2F7%29%2A%28+f+-+s+%29+\"$
\n" ); document.write( " $\"+24+=+%283%2F7%29%2A%28+80+-+24+%29+\"$
\n" ); document.write( " $\"+24+=+%283%2F7%29%2A56+\"$
\n" ); document.write( " $\"+168+=+3%2A56+\"$
\n" ); document.write( " $\"+168+=+168+\"$
\n" ); document.write( "Today my son is the age I was when he was born
\n" ); document.write( " $\"+s+=+m+-+s+\"$
\n" ); document.write( " $\"+24+=+48+-+24+\"$
\n" ); document.write( " $\"+24+=+24+\"$
\n" ); document.write( "In four years he will be exactly 1/3 the age of my father.
\n" ); document.write( "(2) $\"+s+%2B+4+=+%281%2F3%29%2A%28+f%2B4+%29+\"$
\n" ); document.write( "(2) $\"+24+%2B+4+=+%281%2F3%29%2A%28+80%2B4+%29+\"$
\n" ); document.write( "(2) $\"+3%2A28+=+84+\"$
\n" ); document.write( "(2) $\"+84+=+84+\"$
\n" ); document.write( "OK\r
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