document.write( "Question 1190791: Split 69 into three parts such that they are in A. P. and the product of the two smaller parts is 483 \n" ); document.write( "
Algebra.Com's Answer #822500 by ankor@dixie-net.com(22740)\"\" \"About 
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Split 69 into three parts
\n" ); document.write( "a + b + c = 69
\n" ); document.write( " such that they are in A. P.
\n" ); document.write( "Assume this means Arithmetic Progression. (dif between two Nos. is the same)
\n" ); document.write( "let d = difference between consecutive numbers
\n" ); document.write( "Then
\n" ); document.write( "b = a + d
\n" ); document.write( "c = a + 2d
\n" ); document.write( "the product of the two smaller parts is 483
\n" ); document.write( "ab = 483
\n" ); document.write( "replace b with a+d
\n" ); document.write( "a(a+d) = 483
\n" ); document.write( "a^2 + ad = 483
\n" ); document.write( ":
\n" ); document.write( "in the first equation write it
\n" ); document.write( "a + (a+d) + (a+2d) = 69
\n" ); document.write( "3a + 3d = 69
\n" ); document.write( "simplify, divide by 3
\n" ); document.write( "a + d = 23
\n" ); document.write( "d = (23-a)
\n" ); document.write( ":
\n" ); document.write( "Back to a^2 + ad = 83, replace d with (23-a)
\n" ); document.write( "a^2 + a(23-a) = 483
\n" ); document.write( "a^2 + 23a - a^2 = 483
\n" ); document.write( "a^2 drops out
\n" ); document.write( "23a = 483
\n" ); document.write( "a = 21
\n" ); document.write( "Find d
\n" ); document.write( "23-21 = 2 is the difference
\n" ); document.write( "The numbers then are:
\n" ); document.write( "21, 23, 25
\n" ); document.write( ":
\n" ); document.write( "Check:
\n" ); document.write( "21 * 23 = 483
\n" ); document.write( "and
\n" ); document.write( "21 + 23 + 25 = 69 \n" ); document.write( "
\n" );