document.write( "Question 1194795: A woman is 3 times as old as her son. 8 years ago the product of their ages was 112. Find their present ages. \n" ); document.write( "

Algebra.Com's Answer #827068 by MathLover1(20850) $\"\"$ $\"About$

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\n" ); document.write( "let woman’s age be $\"w\"$ and son’s age $\"s\"$ \r
\n" ); document.write( "\n" ); document.write( "if a woman is $\"3\"$ times as old as her son, we have\r
\n" ); document.write( "\n" ); document.write( " $\"w=3s\"$ ..........eq.1\r
\n" ); document.write( "\n" ); document.write( "if $\"+8\"$ years ago the product of their ages was $\"112\"$ \r
\n" ); document.write( "\n" ); document.write( " $\"%28w-8%29%28s-8%29=112\"$
\n" ); document.write( " $\"s+w+-+8+s+-+8+w+%2B+64+=+112\"$
\n" ); document.write( " $\"s+w+-+8+s+-+8+w+-+48+=+0\"$ ........eq.2\r
\n" ); document.write( "\n" ); document.write( "from eq.1 and eq.2 we have
\n" ); document.write( " $\"s+%2A3s+-+8+s+-+8%2A3s+-+48+=+0\"$
\n" ); document.write( " $\"3s%5E2+-+8+s+-+24s+-+48+=+0\"$
\n" ); document.write( " $\"3s%5E2+-+32s+-+48+=+0\"$
\n" ); document.write( " $\"3s%5E2+-+32s+-+48+=+0\"$
\n" ); document.write( " $\"%28s+-+12%29+%283+s+%2B+4%29+=+0\"$ \r
\n" ); document.write( "\n" ); document.write( "we need integer solution, so $\"s=12\"$ \r
\n" ); document.write( "\n" ); document.write( "then
\n" ); document.write( " $\"w=3%2A12\"$ ..........eq.1
\n" ); document.write( " $\"w=36\"$ \r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( " their present ages: woman is $\"36\"$ and son is $\"12\"$ years old\r
\n" ); document.write( "\n" ); document.write( "check the product of their ages $\"+8\"$ years ago\r
\n" ); document.write( "\n" ); document.write( " $\"+8\"$ years ago woman was $\"36-8=28\"$ and son was $\"12-8=4\"$ \r
\n" ); document.write( "\n" ); document.write( " $\"28%2A4=112\"$ which confirms our result\r
\n" ); document.write( "\n" ); document.write( " \n" ); document.write( "

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