Charlene's age in years is 16 more than the number of years in the sum of

Question

Betty and Ashley's ages. The square of Charlene's age is 1632 more than the number of years in the square of the sum of Betty's and Ashley's ages. How many years are in the sum of the two women?

Answer 1

C        = Charlene's age

(B+A) = sum of Betty and Ashley's ages

 

we have two unknowns, C and (B+A) and two givens

 

1st given:

      1)  C = 16 + (B+A)

 

2nd given:

      2)  C^2 = 1632 + (B+A)^2

 

 

if we Square both sides of the 1st equation to get C^2 

we then substitute what we got for C^2 in equation 2.

 

      1)  C^2 = (16 + (B+A))^2

                  = 256 + 32*(B+A) + (B+A)^2

 

Substitute the above for C^2 in the 2nd equation

       -------- 1st eqn sq -----------     ---- 2nd eqn ----

       256 + 32*(B+A) + (B+A)^2 = 1632 + (B+A)^2    (Note the (B+A)^2 now cancel)

 

       256 + 32*(B+A) = 1632      now, just solve for (B+A)

 

        32*(B+A) = 1632 - 256

 

        32*(B+A) = 1376     

 

             (B+A) = 1376/32    OR    B+A = 43   (sum of ages = 43)