document.write( "Question 472729: Half of henry's age added to 1/3 of Daisy's age is 11 years. Six years from now, the sum of their ages will be 40 years. How old is each? \n" ); document.write( "
Algebra.Com's Answer #324066 by Theo(13342)\"\" \"About 
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let x = henry's age.
\n" ); document.write( "let y = daisy's age.
\n" ); document.write( "half of henry's age added to 1/3 of daisy's age is equal to 11.
\n" ); document.write( "in equation form, this becomes:
\n" ); document.write( "x/2 + y/3 = 11
\n" ); document.write( "6 years from now the sum of their ages will be 40.
\n" ); document.write( "in equation form, this becomes:
\n" ); document.write( "(x+6) + (y+6) = 40
\n" ); document.write( "if we multiply the first equation by 6, then we get:
\n" ); document.write( "3x + 2y = 66
\n" ); document.write( "that removes the fractions from the first equation.
\n" ); document.write( "if we simplify the second equation by combining like terms, we get:
\n" ); document.write( "x + y + 12 = 40
\n" ); document.write( "if we subtract 12 from both sides of this equation, we get:
\n" ); document.write( "x + y = 28
\n" ); document.write( "solving for y, we get:
\n" ); document.write( "y = 28 - x
\n" ); document.write( "we replace y with 28 - x in the first equation to get:
\n" ); document.write( "3x + 2y = 66 becomes:
\n" ); document.write( "3x + 2 * (28-x) = 66
\n" ); document.write( "now we have one equation in one unknown which we can solve for.
\n" ); document.write( "simplify this equation to get:
\n" ); document.write( "3x + 56 - 2x = 66
\n" ); document.write( "combine like terms to get:
\n" ); document.write( "x + 56 = 66
\n" ); document.write( "subtract 56 from both sides of this equation to get:
\n" ); document.write( "x = 10
\n" ); document.write( "substitute for x in the equation of x + y = 28 to get:
\n" ); document.write( "y = 28 - x which becomes:
\n" ); document.write( "y = 28 - 10 which becomes:
\n" ); document.write( "y = 18
\n" ); document.write( "we have x = 10 and y = 18
\n" ); document.write( "this means:
\n" ); document.write( "henry's age is 10
\n" ); document.write( "daisy's age is 18
\n" ); document.write( "half of henry's age added to 1/3 of daisy's age is equal to 11.
\n" ); document.write( "half of henry's age is 5.
\n" ); document.write( "one third of daisy's age is 6
\n" ); document.write( "5 + 6 = 11
\n" ); document.write( "so far so good.
\n" ); document.write( "6 years from now the sum of their ages will be 40.
\n" ); document.write( "6 years from now, henry is 16.
\n" ); document.write( "6 years from now, daisy is 24.
\n" ); document.write( "16 + 24 = 40.
\n" ); document.write( "both requirements of the problem are solved, so the solutions are good.
\n" ); document.write( "henry is 10 years old.
\n" ); document.write( "daisy is 18 years old.\r
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