Ben Better is 5 years older than his sister Ima. All they will tell you is that the sum of the squares of their age is 773. How old are they?

17 and 22yrs

Step-by-step explanation:

Given parameters:

 Let Ben's age  = B

  Let Ima's age  = L

   B = L + 5 i

Also,

  the square of their age is 773;

          B²  + L² = 773 ---ii

To find their ages, substitute equation i into ii;

           (L + 5)² + L² = 773

           L² + 10L + 25 + L² = 773

           2L² + 10L + 25 = 773

           2L² + 10L + 25 - 773 = 0

            2L² + 10L -748 = 0

  Divide through by 2;

              L² + 5L - 374 = 0

              L² + 22L - 17L - 374 = 0

           L(L + 22) - 17(L + 22) = 0

           (L - 17)(L + 22) = 0

           L = 17 or -22

Age cannot be -22;

  Ima's age  = 17

  Ben's age;

         B = L + 5

         B = 17 + 5  = 22

i think this could be a possible answer (1 / 84) -1

good luck! : d