SOLUTION: 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

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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
Answer by ikleyn(52790)   (Show Source): You can put this solution on YOUR website!
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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 Hannah's age and 2 times Lucy's age is 90. Find Lucy's present age
~~~~~~~~~~~~~ 

Let x = Lucy's age.

Then Hannah's age is 90-2x years.


Next you have this equation

    x^2 + (90-2x)^2 = 30*(x + (90-2x)).


Simplify step by step and find x

    x^2 + 8100 - 360x + 4x^2 = 30*(90-x)

    5x^2 - 360x + 8100 = 2700 - 30x

    5x^2 - 330x + 5400 = 0

     x^2 -  66x + 1080 = 0.


Solve this quadratic equation by any way you can. Its roots are 30 and 36.


Now let analyze them.


If x= 30 is Lucy's age, then Hannah's age is 90-2x = 90-2*30 = 30,
and Lucy can not be the older sister.


If x= 36 is Lucy's age, then Hannah's age is  90-2x = 90-2*36 = 18 years,
and it satisfies the condition requirements.


ANSWER.  Lucy is 36 years old.

Solved.



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