document.write( "Question 283474: Find two numbers whose sum is 55 and product is 600. \n" ); document.write( "

Algebra.Com's Answer #205750 by oberobic(2304) $\"\"$ $\"About$

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\"Two numbers\" suggests we use 'x' and 'y'.
\n" ); document.write( "However, we are told they sum to 55: x + y = 55
\n" ); document.write( "That means we can substitute 55-x for y.
\n" ); document.write( "That, in turn, means we have only one unknown to solve.
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\n" ); document.write( "We also are told that x*y = 600
\n" ); document.write( "Substituting y = 55-x
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\n" ); document.write( "x*(55-x) = 600
\n" ); document.write( "55x -x^2 = 600
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\n" ); document.write( "Add x^2 to both sides
\n" ); document.write( "55x = x^2 + 600
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\n" ); document.write( "Subtract 55x from both sides
\n" ); document.write( "0 = x^2 -55x + 600
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\n" ); document.write( "Factor
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\n" ); document.write( "(x-15)(x-40)=0
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\n" ); document.write( "So we we have two possible values for x: 15 and 40.
\n" ); document.write( "That means we have two possible values for y:
\n" ); document.write( "55-15 = 40 and
\n" ); document.write( "55-40 = 15.
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\n" ); document.write( "Answer:
\n" ); document.write( "The two numbers are 15 and 40. Their sum is 55. Their product is 600.
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\n" ); document.write( "Done. \n" ); document.write( "

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