document.write( "Question 572991: A mother is 3 times as old as her daughter. Seven years ago, she was 5 times as old. How old are the mother and daughter now? \n" ); document.write( "

Algebra.Com's Answer #368720 by mathsmiles(68) $\"\"$ $\"About$

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\n" ); document.write( "Let's let M = mother's age now.
\n" ); document.write( "D = daughter's age now.\r
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\n" ); document.write( "\n" ); document.write( "M = 3 x D\r
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\n" ); document.write( "\n" ); document.write( "Seven years ago, mother was M-7 years old; daughter was D-7 years old
\n" ); document.write( "At that time, mother was 5 times daughter's age.\r
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\n" ); document.write( "\n" ); document.write( "M-7 = 5(D-7)\r
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\n" ); document.write( "\n" ); document.write( "Substituting from the previous equation for mother's age:\r
\n" ); document.write( "\n" ); document.write( "(3D)-7 = 5(D-7) Multiplying out to remove the parens:
\n" ); document.write( "3D - 7 = 5D - 35
\n" ); document.write( "Subtract 3D from both sides of the equation:
\n" ); document.write( "-7 = 2D -35
\n" ); document.write( "Add 35 to both sides of the equation:
\n" ); document.write( "28 = 2D
\n" ); document.write( "Divide both sides by 2
\n" ); document.write( "14 = D\r
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\n" ); document.write( "\n" ); document.write( "Daughter is 14, mother is 3 times her age, so 14x3 = 42\r
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\n" ); document.write( "\n" ); document.write( "Checking:
\n" ); document.write( "Seven years ago, daughter was 7, mother was 35. Mother was 5 times as old as daughter. Correct!\r
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