document.write( "Question 607031: The sum of the ages of a man and his wife is 80 years. 10 years ago, the ages of the wife was exactly two-third the age of the man. Find the present ages of the man and his wife. \n" ); document.write( "

Algebra.Com's Answer #382353 by sophxmai(62) $\"\"$ $\"About$

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The sum of the ages of a man and his wife is 80 years. 10 years ago, the ages of the wife was exactly two-third the age of the man. Find the present ages of the man and his wife.\r
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\n" ); document.write( "\n" ); document.write( "Let:
\n" ); document.write( "man's age = x
\n" ); document.write( "wife's age = y\r
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\n" ); document.write( "\n" ); document.write( "x+y=80 <--sum of their age
\n" ); document.write( "y-10=2/3x <--10 years ago, the age of the woman was 2/3 of the man's current age\r
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\n" ); document.write( "\n" ); document.write( "y=2/3x+10 <--solve the 2nd equation for y
\n" ); document.write( "x+2/3x+10=80 <--plug above into 1st equation
\n" ); document.write( "5/3x=70 <--simplify and solve
\n" ); document.write( "x=42 <--plug back into original equation to find y
\n" ); document.write( "42+y=80
\n" ); document.write( "y=80-42
\n" ); document.write( "y=38\r
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\n" ); document.write( "\n" ); document.write( "Since x=42 and y=38
\n" ); document.write( "The man's age is 42 and the wife's age is 38 \n" ); document.write( "

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