document.write( "Question 1012475: the sum of two numbers is 7 times their difference. the difference of their squares is twice their sum. find the numbers. \n" ); document.write( "
Algebra.Com's Answer #628422 by ankor@dixie-net.com(22740)\"\" \"About 
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the sum of two numbers is 7 times their difference.
\n" ); document.write( "a + b = 7(a-b)
\n" ); document.write( "a + b = 7a - 7b
\n" ); document.write( "b + 7b = 7a - a
\n" ); document.write( "8b = 6a
\n" ); document.write( "simplify, divide by 2
\n" ); document.write( "4b = 3a
\n" ); document.write( "b = 3a/4
\n" ); document.write( "b = .75a
\n" ); document.write( ":
\n" ); document.write( "the difference of their squares is twice their sum.
\n" ); document.write( "a^2 - b^2 = 2(a + b)
\n" ); document.write( "a^2 - b^2 = 2a + 2b
\n" ); document.write( "substitute for b
\n" ); document.write( "a^2 - (.75a)^2 = 2a + 2(.75a)
\n" ); document.write( "a^2 - .5625a^2 = 2a + 1.5a
\n" ); document.write( "Divide equation by a
\n" ); document.write( "a - .5625a = 2 + 1.5
\n" ); document.write( ".4375a = 3.5
\n" ); document.write( "a = 3.5/.4375
\n" ); document.write( "a = 8
\n" ); document.write( "Find b
\n" ); document.write( "b = .75(8)
\n" ); document.write( "b = 6
\n" ); document.write( ":
\n" ); document.write( " find the numbers. 8 & 6
\n" ); document.write( ":
\n" ); document.write( ":
\n" ); document.write( ":
\n" ); document.write( "See if this checks out
\n" ); document.write( "8 + 6 = 7(8 - 6)
\n" ); document.write( "14 = 7(2)
\n" ); document.write( "and
\n" ); document.write( "8^2 - 6^2 = 2(8+6)
\n" ); document.write( "64 - 36 = 2(14) \n" ); document.write( "
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