document.write( "Question 842605: Karen is 5 years older than Sean. The product of their ages is 300. How old is Karen? \n" ); document.write( "

Algebra.Com's Answer #507655 by thejackal(72) $\"\"$ $\"About$

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if karens age is x, and we know that karen is seans age + 5 lets form an equation.\r
\n" ); document.write( "\n" ); document.write( "let seans age be y such that y + 5 = x\r
\n" ); document.write( "\n" ); document.write( "if y * (y + 5) = 300 find the value of x\r
\n" ); document.write( "\n" ); document.write( "solve for y first\r
\n" ); document.write( "\n" ); document.write( "y^2 + 5y = 300\r
\n" ); document.write( "\n" ); document.write( "we now have a quadratic equation\r
\n" ); document.write( "\n" ); document.write( "y^2 + 5y - 300 = 0\r
\n" ); document.write( "\n" ); document.write( "You can solve it using any of the known methods: perhaps the easiest here would be the quadratic formula.\r
\n" ); document.write( "\n" ); document.write( " $\"x+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+\"$ \r
\n" ); document.write( "\n" ); document.write( "a = 1; b = +5; c = -300\r
\n" ); document.write( "\n" ); document.write( "the result will be the roots -20 and 15; since age can't be less than 0 we can discard the first root.\r
\n" ); document.write( "\n" ); document.write( "so seans age is 15 and therefore karens age is 15+5 = 20 years\r
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