document.write( "Question 220494: The difference between two numbers is 16. Three times the larger number is 9 times the smaller. What are the numbers? \n" ); document.write( "
Algebra.Com's Answer #165776 by likaaka(51)\"\" \"About 
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You must set up a system of equations. Begin by naming your variables ie.
\n" ); document.write( "x is one number and y is the other
\n" ); document.write( "If the difference (which is subtraction) of the two numbers is 16, your first equation is x-y=16
\n" ); document.write( "If the larger number times 3, which is x according to the first equation, is equal to 9 times the smaller, your second equation is 3x=9y
\n" ); document.write( "Here is your system of equations
\n" ); document.write( "x-y=16
\n" ); document.write( "3x=9y
\n" ); document.write( "First, solve for x in terms of y by adding y to both sides of the first equation
\n" ); document.write( "x-y +y=16 +y, now simplify
\n" ); document.write( "x=16+y
\n" ); document.write( "Now substitute the value of x into the second equation to solve
\n" ); document.write( "3(16+y)=9y, distribute the 3
\n" ); document.write( "48+3y=9y, move all y to one side by subtracting 3y from both sides
\n" ); document.write( "48+3y -3y=9y -3y, simplify
\n" ); document.write( "48=6y, solve for y by dividing both sides by 6
\n" ); document.write( "48/6=(6y)/6, simplify
\n" ); document.write( "y=8, so the smaller number is 8 now solve for x
\n" ); document.write( "x=16+y
\n" ); document.write( "x+16+8
\n" ); document.write( "x=24, the larger number is 24\r
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