document.write( "Question 1193983: Hannah has an older sister Lucy. It is known that the sum of the squares of their ages give a number equal to 30 times the sum of their ages Given also that the sum of Hannahs age and 2 times Lucys age is 90. Find Lucys present age \n" ); document.write( "

Algebra.Com's Answer #826064 by ikleyn(52790) $\"\"$ $\"About$

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\n" ); document.write( "Hannah has an older sister Lucy. It is known that the sum of the squares of their ages
\n" ); document.write( "give a number equal to 30 times the sum of their ages. Given also that the sum
\n" ); document.write( "of Hannah's age and 2 times Lucy's age is 90. Find Lucy's present age
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document.write( "Let x = Lucy's age.\r\n" );
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document.write( "Then Hannah's age is 90-2x years.\r\n" );
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document.write( "Next you have this equation\r\n" );
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document.write( "    x^2 + (90-2x)^2 = 30*(x + (90-2x)).\r\n" );
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document.write( "Simplify step by step and find x\r\n" );
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document.write( "    x^2 + 8100 - 360x + 4x^2 = 30*(90-x)\r\n" );
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document.write( "    5x^2 - 360x + 8100 = 2700 - 30x\r\n" );
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document.write( "    5x^2 - 330x + 5400 = 0\r\n" );
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document.write( "     x^2 -  66x + 1080 = 0.\r\n" );
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document.write( "Solve this quadratic equation by any way you can. Its roots are 30 and 36.\r\n" );
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document.write( "Now let analyze them.\r\n" );
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document.write( "If x= 30 is Lucy's age, then Hannah's age is 90-2x = 90-2*30 = 30,\r\n" );
document.write( "and Lucy can not be the older sister.\r\n" );
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document.write( "If x= 36 is Lucy's age, then Hannah's age is  90-2x = 90-2*36 = 18 years,\r\n" );
document.write( "and it satisfies the condition requirements.\r\n" );
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document.write( "ANSWER.  Lucy is 36 years old.\r\n" );
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