document.write( "Question 1034779: Mum is 4 times older than her daughter. In 4 years time she will be 3 times older than her daughter. In how many years will mum be exactly twice her daughters age? What will their ages be? \n" ); document.write( "

Algebra.Com's Answer #649451 by josmiceli(19441) $\"\"$ $\"About$

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Let $\"+m+\"$ = Mum's age now
\n" ); document.write( "Let $\"+d+\"$ = daughter's age now
\n" ); document.write( "---------------------------
\n" ); document.write( "(1) $\"+m+=+4d+\"$
\n" ); document.write( "(2) $\"+m+%2B+4++=+3%2A%28+d+%2B+4+%29+\"$
\n" ); document.write( "-------------------------
\n" ); document.write( "Substitute (1) into (2)
\n" ); document.write( "(2) $\"+4d+%2B+4++=+3%2A%28+d+%2B+4+%29+\"$
\n" ); document.write( "(2) $\"+4d+%2B+4+=+3d+%2B+12+\"$
\n" ); document.write( "(2) $\"+d+=+8+\"$
\n" ); document.write( "and
\n" ); document.write( "(1) $\"+m+=+4d+\"$
\n" ); document.write( "(1) $\"+m+=+4%2A8+\"$
\n" ); document.write( "(1) $\"+m+=+32+\"$
\n" ); document.write( "--------------------
\n" ); document.write( "Let $\"+x+\"$ = the number of years from now
\n" ); document.write( "when Mum's age is twice daughter's age
\n" ); document.write( "--------------------
\n" ); document.write( "(3) $\"+m+%2B+x++=+2%2A%28+d+%2B+x+%29+\"$
\n" ); document.write( "(3) $\"+32+%2B+x++=+2%2A%28+8+%2B+x+%29+\"$
\n" ); document.write( "(3) $\"+32+%2B+x+=+16+%2B+2x+\"$
\n" ); document.write( "(3) $\"+x+=+16+\"$
\n" ); document.write( "In 16 years Mum will be twice daughter's age
\n" ); document.write( "--------------------
\n" ); document.write( "check:
\n" ); document.write( " $\"+32+%2B+16+=+48+\"$
\n" ); document.write( "and
\n" ); document.write( " $\"+8+%2B+16+=+24+\"$
\n" ); document.write( "48 is twice 24
\n" ); document.write( "OK \n" ); document.write( "

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