document.write( "Question 179541: in four years time a mother will be three times old as her son. four years ago she was five times as old as her son. find their present age \n" ); document.write( "

Algebra.Com's Answer #134486 by josmiceli(19441) $\"\"$ $\"About$

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Let $\"m\"$ = the Mother's age now
\n" ); document.write( "Let $\"s\"$ = her Son's age now
\n" ); document.write( "In 4 years, the Mother's age will be $\"m+%2B+4\"$
\n" ); document.write( "In 4 years, the Son age will be $\"s+%2B+4\"$
\n" ); document.write( "4 years ago, the Mother's age was $\"m+-+4\"$
\n" ); document.write( "4 years ago, the Son's age was $\"s+-+4\"$
\n" ); document.write( "given:
\n" ); document.write( "(1) $\"m+%2B+4+=+3%2A%28s+%2B+4%29\"$
\n" ); document.write( "(2) $\"m+-+4+=+5%2A%28s+-+4%29\"$
\n" ); document.write( "-----------------------
\n" ); document.write( "There are 2 equations and 2 unknowns, so it's solvable
\n" ); document.write( "(1) $\"m+%2B+4+=+3s+%2B+12\"$
\n" ); document.write( "(2) $\"m+-+4+=+5s+-+20\"$
\n" ); document.write( "Now subtract (1) from (2)
\n" ); document.write( "(2) $\"m+-+4+=+5s+-+20\"$
\n" ); document.write( "(1) $\"-m+-+4+=+-3s+-+12\"$
\n" ); document.write( " $\"-8+=+2s+-+32\"$
\n" ); document.write( " $\"2s+=+24\"$
\n" ); document.write( " $\"s+=+12\"$
\n" ); document.write( "Substitute this in (2)
\n" ); document.write( "(2) $\"m+-+4+=+5%2A12+-+20\"$
\n" ); document.write( " $\"m+-+4+=+60+-+20\"$
\n" ); document.write( " $\"m+-+4+=+40\"$
\n" ); document.write( " $\"m+=+44\"$
\n" ); document.write( "The Mother is 44 and the Son is 12
\n" ); document.write( "check:
\n" ); document.write( "(1) $\"m+%2B+4+=+3%2A%28s+%2B+4%29\"$
\n" ); document.write( "(1) $\"44+%2B+4+=+3%2A%2812+%2B+4%29\"$
\n" ); document.write( " $\"48+=+48\"$
\n" ); document.write( "(2) $\"m+-+4+=+5%2A%28s+-+4%29\"$
\n" ); document.write( "(2) $\"44+-+4+=+5%2A%2812+-+4%29\"$
\n" ); document.write( " $\"40+=+40\"$
\n" ); document.write( "OK \n" ); document.write( "

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