document.write( "Question 131565: Olivia, Newt, and John were each born 3 years apart, with Olivia the youngest and john the oldest. The sum of the squares of their ages is 606. How old is each? \n" ); document.write( "

Algebra.Com's Answer #96040 by solver91311(24713) $\"\"$ $\"About$

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Olivia is x years old, so Newt is x + 3, and John is x + 6.\r
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\n" ); document.write( "\n" ); document.write( "The sum of the squares of their ages: $\"x%5E2%2B%28x%2B3%29%5E2%2B%28x%2B6%29%5E2\"$ is equal to 606, so expand, collect terms, put it in standard form, and solve:\r
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\n" ); document.write( "\n" ); document.write( " $\"x%5E2%2Bx%5E2%2B6x%2B9%2Bx%5E2%2B12x%2B36=606\"$
\n" ); document.write( " $\"3x%5E2%2B18x%2B45=606\"$
\n" ); document.write( " $\"3x%5E2%2B18x-561=0\"$ \r
\n" ); document.write( "\n" ); document.write( "Note that 5 + 6 + 1 = 12 and 12 is evenly divisible by 3, so 561 is evenly divisible by 3.\r
\n" ); document.write( "\n" ); document.write( "Divide through by 3
\n" ); document.write( " $\"x%5E2%2B6x-187=0\"$ \r
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\n" ); document.write( "\n" ); document.write( " $\"-187+=+-11+%2A+17\"$ and $\"-11+%2B+17+=+6\"$ , so:\r
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\n" ); document.write( "\n" ); document.write( " $\"%28x-11%29%28x%2B17%29=0\"$ , therefore $\"x=11\"$ or $\"x=-17\"$ . -17 for the age of a person is absurd (since the problem statement contains the words 'were born') so we must have introduced an extraneous root when we squared the variable setting up the problem in the first place. Exclude -17, and Olivia's age must be 11. That means that Newt is 14 and John is 17.\r
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\n" ); document.write( "\n" ); document.write( "Check:
\n" ); document.write( " $\"11%5E2%2B14%5E2%2B17%5E2=121%2B196%2B289=606\"$ answer checks. \n" ); document.write( "

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