document.write( "Question 91663: A mother is 30 years older than her daughter. Five years ago she was four times as old as her daughter. How old are they now? \n" ); document.write( "
Algebra.Com's Answer #66568 by Earlsdon(6294)\"\" \"About 
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Start by assigning variables to the unknown quantities:
\n" ); document.write( "Let M = Mother's present age.
\n" ); document.write( "Let D = Daughter's present age.
\n" ); document.write( "From the problem description we can write:
\n" ); document.write( " Mother's age is (M) is (=) 30 years older than her daughter's age, so:
\n" ); document.write( "M = D+30
\n" ); document.write( "Five years ago, Mother's age (M-5) was (=) four times her daughter's age, so
\n" ); document.write( "M-5 = 4(D-5) Simplify.
\n" ); document.write( "M-5 = 4D-20 Rewrite this as: (add 5 to both sides)
\n" ); document.write( "M = 4D-15 now substitute this for the M in the first equation.
\n" ); document.write( "D+30 = 4D-15 Simplify and solve for D by adding 15 to both sides.
\n" ); document.write( "D+45 = 4D Now subtract D from both sides.
\n" ); document.write( "45 = 3D Finally, divide both sides by 3.
\n" ); document.write( "15 = D or D = 15 This is the daughter's present age.
\n" ); document.write( "M = D+30
\n" ); document.write( "M = 15+30
\n" ); document.write( "M = 45 This is the mother's present age.
\n" ); document.write( "Check:
\n" ); document.write( "M = D+30
\n" ); document.write( "M = 15+30
\n" ); document.write( "M = 45
\n" ); document.write( "Five years ago:
\n" ); document.write( "M-5 = 4(D-5)
\n" ); document.write( "45-5 = 4(15-5)
\n" ); document.write( "40 = 4(10)
\n" ); document.write( "40 = 40\r
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