document.write( "Question 218793: A father is 32 years old and his daughter is 2 years old. He is now 16 times as old as his daughter. In how many years will he be only 4 times as old? \n" ); document.write( "

Algebra.Com's Answer #164706 by josmiceli(19441) $\"\"$ $\"About$

You can put this solution on YOUR website!
The big thing to notice here is that the difference
\n" ); document.write( "in their ages never changes
\n" ); document.write( "Let $\"f\"$ = Father's age
\n" ); document.write( "Let $\"d\"$ = Daughter's age
\n" ); document.write( " $\"d+=+f+-+30\"$ (always)
\n" ); document.write( "This is a ratio problem, so
\n" ); document.write( " $\"f%2Fd+=+4%2F1\"$ (4 times as old)
\n" ); document.write( "And, rewriting:
\n" ); document.write( " $\"f%2F%28f-30%29+=+4%2F1\"$
\n" ); document.write( "Multiply both sides by $\"f-30\"$
\n" ); document.write( " $\"f+=+4%2A%28f-30%29\"$
\n" ); document.write( " $\"f+=+4f+-+120\"$
\n" ); document.write( " $\"3f+=+120\"$
\n" ); document.write( " $\"f+=+40\"$
\n" ); document.write( " $\"d+=+10\"$
\n" ); document.write( "The Father will be 40 when he's 4 times as old as his Daughter
\n" ); document.write( "and that will be in 8 years since he's 32 now.
\n" ); document.write( "Notice that the fact that he was 16 times as old as his Daughter
\n" ); document.write( "when he was 32 was just thrown in to confuse you \n" ); document.write( "

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