document.write( "Question 733591: two girls' ages, 11 years apart, when multiplied, make 210. The sum of their ages is? \n" ); document.write( "

Algebra.Com's Answer #448487 by MathLover1(20850) $\"\"$ $\"About$

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let one girl's be $\"x\"$ and another $\"y\"$
\n" ); document.write( "if two girls' ages, $\"11\"$ years apart, then $\"x-y=11\"$ ...eq.1\r
\n" ); document.write( "\n" ); document.write( "when multiplied, $\"x%2Ay=210\"$ .......eq.2\r
\n" ); document.write( "\n" ); document.write( " The sum of their ages is $\"x%2By\"$ \r
\n" ); document.write( "\n" ); document.write( "start with:\r
\n" ); document.write( "\n" ); document.write( " $\"x-y=11\"$ ...eq.1\r
\n" ); document.write( "\n" ); document.write( " $\"x%2Ay=210\"$ .......eq.2
\n" ); document.write( "____________________________\r
\n" ); document.write( "\n" ); document.write( " $\"x-y=11\"$ ...eq.1...solve for $\"y\"$ \r
\n" ); document.write( "\n" ); document.write( " $\"x-11=y\"$ ...eq.1...substitute $\"y\"$ in eq.2\r
\n" ); document.write( "\n" ); document.write( " $\"x%2A%28x-11%29=210\"$ .......eq.2.....solve for $\"y\"$ \r
\n" ); document.write( "\n" ); document.write( " $\"x%5E2-11x=210\"$ \r
\n" ); document.write( "\n" ); document.write( " $\"x%5E2-11x-210=0\"$ ......use quadratic formula\r
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\n" ); document.write( "\n" ); document.write( " $\"x+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+\"$ \r
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\n" ); document.write( "\n" ); document.write( " $\"x+=+%28-%28-11%29+%2B-+sqrt%28%28-11%29%5E2-4%2A1%2A%28-210%29+%29%29%2F%282%2A1%29+\"$ \r
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\n" ); document.write( "\n" ); document.write( " $\"x+=+%2811+%2B-+sqrt%28121%2B840%29+%29%29%2F2+\"$ \r
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\n" ); document.write( "\n" ); document.write( " $\"x+=+%2811+%2B-+sqrt%28961%29+%29%29%2F2+\"$ \r
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\n" ); document.write( "\n" ); document.write( " $\"x+=+%2811+%2B-+31+%29%29%2F2+\"$ \r
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\n" ); document.write( "\n" ); document.write( "solutions:\r
\n" ); document.write( "\n" ); document.write( " $\"x+=+%2811+%2B+31+%29%2F2+\"$ \r
\n" ); document.write( "\n" ); document.write( " $\"x+=+42%2F2+\"$ \r
\n" ); document.write( "\n" ); document.write( " $\"highlight%28x+=+21+%29\"$ \r
\n" ); document.write( "\n" ); document.write( "and\r
\n" ); document.write( "\n" ); document.write( " $\"x+=+%2811+-31+%29%2F2+\"$ \r
\n" ); document.write( "\n" ); document.write( " $\"x+=+-20%2F2+\"$ \r
\n" ); document.write( "\n" ); document.write( " $\"x+=+-10+\"$ .....since we are looking for age, we do not need this solution\r
\n" ); document.write( "\n" ); document.write( "now find $\"y\"$ \r
\n" ); document.write( "\n" ); document.write( " $\"x-11=y\"$ \r
\n" ); document.write( "\n" ); document.write( " $\"21-11=y\"$ \r
\n" ); document.write( "\n" ); document.write( " $\"highlight%2810=y%29\"$ \r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "so, one girl's be $\"highlight%28x+=+21+%29\"$ and another $\"highlight%2810=y%29\"$ and the sum of their ages is $\"x%2By=21%2B10=highlight%2831%29\"$
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