document.write( "Question 246730: I have chosen three numbers. The second is twice the first, and the third is three times the second. The sum of the first two when multiplied by the sum of the last two happens to be the same as the first number multiplied by the square of the second number. What are the three numbers? \n" ); document.write( "
Algebra.Com's Answer #180254 by ankor@dixie-net.com(22740)\"\" \"About 
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I have chosen three numbers.
\n" ); document.write( "x, y, z
\n" ); document.write( ":
\n" ); document.write( "The second is twice the first,
\n" ); document.write( "y=2x
\n" ); document.write( "or
\n" ); document.write( "x=.5y
\n" ); document.write( ":
\n" ); document.write( "the third is three times the second.
\n" ); document.write( "z = 3y
\n" ); document.write( ":
\n" ); document.write( "The sum of the first two when multiplied by the sum of the last two happens to be the same as the first number multiplied by the square of the second number.
\n" ); document.write( "(x+y)*(y+z) = x * y^2
\n" ); document.write( "Substitute for x and z
\n" ); document.write( "(.5y + y)* (y + 3y) = .5y * y^2
\n" ); document.write( "1.5y * 4y = .5y^3
\n" ); document.write( "6y^2 = .5y^3
\n" ); document.write( "Mult by 2
\n" ); document.write( "12y^2 = y^3
\n" ); document.write( "Divide both sides by y^2
\n" ); document.write( "12 = y
\n" ); document.write( "then
\n" ); document.write( "z = 3(12)
\n" ); document.write( "z = 36
\n" ); document.write( "and
\n" ); document.write( "x = .5(12)
\n" ); document.write( "x = 6
\n" ); document.write( ":
\n" ); document.write( "Check solution in original equation
\n" ); document.write( "(x+y)*(y+z) = x * y^2
\n" ); document.write( "(6+12)*(12+36) = 6 * 12^2
\n" ); document.write( "18 * 48 = 6 * 144
\n" ); document.write( "864 = 864
\n" ); document.write( ":
\n" ); document.write( " What are the three numbers? 6, 12, 36 \n" ); document.write( "
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