Question 216275
Molly's age is twice Anita's. If the sum of the square of their ages is 80, what are their ages?


Step 1.  Let x be Anita's age


Step 2.  Let 2x be Molly's age since it's twice Anita's


Step 3.  Then {{{x^2+(2x)^2=80}}} since the sum of the square of their ages is 80.


Step 4.  Simplifying {{{5x^2=80}}} or {{{x^2=16}}}.  


Step 5.  Taking the square root to both sides of the equation yields {{{x=4}}}. Then 2x=8.


Check...{{{4^2+8^2=16+64=80}}}...which is a true statement


Step 6.  ANSWER:  Anita is 4 years old and Molly is 8 years old.


I hope the above steps were helpful.


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Good luck in your studies!


Respectfully,
Dr J