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The product of two numbers is 1400. If three is subtracted from each number, their product becomes 1175. Find the bigger number.
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\n" ); document.write( "Let x = one number
\n" ); document.write( "and y = second number
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\n" ); document.write( "From: \"The product of two numbers is 1400.\"
\n" ); document.write( "xy = 1400 (equation 1)
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\n" ); document.write( "From: \"If three is subtracted from each number, their product becomes 1175.\"
\n" ); document.write( "(x-3)(y-3) = 1175 (equation 2)
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\n" ); document.write( "solve equation 1 for x:
\n" ); document.write( "xy = 1400
\n" ); document.write( "x = 1400/y
\n" ); document.write( "substitute above into equation 2 and solve for y:
\n" ); document.write( "(x-3)(y-3) = 1175
\n" ); document.write( "(1400/y-3)(y-3) = 1175
\n" ); document.write( "multiplying both sides by y:
\n" ); document.write( "(1400-3y)(y-3) = 1175y
\n" ); document.write( "1400y-4200-3y^2+9y = 1175y
\n" ); document.write( "1409y-4200-3y^2 = 1175y
\n" ); document.write( "-3y^2+1409y-4200 = 1175y
\n" ); document.write( "-3y^2+234y-4200 = 0
\n" ); document.write( "3y^2-234y+4200 = 0
\n" ); document.write( "y^2-78y+1400 = 0
\n" ); document.write( "(y-28)(y-50) = 0
\n" ); document.write( "y = {28, 50}
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\n" ); document.write( "Answer: 50\r
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