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x = age of rice today.
\n" ); document.write( "y = age of dandy today.
\n" ); document.write( "three years ago, rice was 3 times as old as dandy.
\n" ); document.write( "equation for that is:
\n" ); document.write( "x-3 = 3*(y-3)
\n" ); document.write( "today she is twice as old.
\n" ); document.write( "equation for that is x = 2*y
\n" ); document.write( "you have two equations that need to be solved simultaneously.
\n" ); document.write( "they are:
\n" ); document.write( "x = 2*y
\n" ); document.write( "x-3 = 3*(y-3)
\n" ); document.write( "simplify the second equation and leave the first equation as is to get:
\n" ); document.write( "x = 2y
\n" ); document.write( "x-3 = 3y-9
\n" ); document.write( "in the first equation, subtract 2y from both sides to get:
\n" ); document.write( "x - 2y = 0
\n" ); document.write( "in the second equation, subtract 3y from both sides and add 3 to both sides to get:
\n" ); document.write( "x - 3y = -6
\n" ); document.write( "your two equations are now:
\n" ); document.write( "x - 2y = 0
\n" ); document.write( "x - 3y = -6
\n" ); document.write( "subtract the second equation from the first to get:
\n" ); document.write( "y = 6
\n" ); document.write( "you were given that x = 2y, therefore x = 12
\n" ); document.write( "you have x = 12 and y = 6
\n" ); document.write( "you are given that x = 2y which becomes 12 = 2*6 which becomes 12 = 12 which is true.
\n" ); document.write( "you are given that x-3 = 3*(y-3) which becomes 12-3 = 3*(6-3) which becomes 9 = 3*3 which becomes 9 = 9 which is true.
\n" ); document.write( "both equations are true when x = 12 and y = 6
\n" ); document.write( "your solution is that rica is 12 years old and dandy is 6.\r
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