document.write( "Question 232430: A mother is 25 years older than her daughter. Five years ago, the daughter was half as old as the mother was then. How old is the daughter now? \n" ); document.write( "

Algebra.Com's Answer #171768 by josmiceli(19441) $\"\"$ $\"About$

You can put this solution on YOUR website!
Let $\"m\"$ = Mother's age now
\n" ); document.write( "Let $\"d\"$ = Daughter's age now
\n" ); document.write( " $\"m+-+5\"$ = Mother's age $\"5\"$ years ago
\n" ); document.write( " $\"d+-+5\"$ = Daughter's age $\"5\"$ years ago
\n" ); document.write( "given:
\n" ); document.write( "(1) $\"m+=+d+%2B+25\"$
\n" ); document.write( "(2) $\"d+-+5+=+%281%2F2%29%2A%28m+-+5%29\"$
\n" ); document.write( "--------------------------------
\n" ); document.write( "This is 2 equations and 2 unknowns, so it's solvable
\n" ); document.write( "Multiply both sides of (2) by $\"2\"$
\n" ); document.write( "(2) $\"2%2A%28d+-+5%29+=+m+-+5\"$
\n" ); document.write( "(2) $\"2d+-+10+=+m+-+5\"$
\n" ); document.write( "(2) $\"2d+-+m+=+5\"$
\n" ); document.write( "Subtract $\"d\"$ from both sides of (1)
\n" ); document.write( "(1) $\"-d+%2B+m+=+25\"$
\n" ); document.write( "Add (1) and (2)
\n" ); document.write( "(2) $\"2d+-+m+=+5\"$
\n" ); document.write( "(1) $\"-d+%2B+m+=+25\"$
\n" ); document.write( " $\"d+=+30\"$
\n" ); document.write( "The daughter is 30 years old
\n" ); document.write( "check answer:
\n" ); document.write( "(1) $\"m+=+d+%2B+25\"$
\n" ); document.write( "(1) $\"m+=+d+%2B+25\"$
\n" ); document.write( " $\"m+=+55\"$
\n" ); document.write( "(2) $\"d+-+5+=+%281%2F2%29%2A%28m+-+5%29\"$
\n" ); document.write( "(2) $\"30+-+5+=+%281%2F2%29%2A%28m+-+5%29\"$
\n" ); document.write( "(2) $\"25+=+%281%2F2%29%2A%2855+-+5%29\"$
\n" ); document.write( " $\"25+=+%281%2F2%29%2A50\"$
\n" ); document.write( " $\"25+=+25\"$
\n" ); document.write( "OK\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( " \n" ); document.write( "

\n" );