SOLUTION: If you add the square of Tom's age to the age of Mary, the sum is 62; but if you add the square of Mary's age to the age of Tom, the result is 176. What is the difference between i

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Question 1162907: If you add the square of Tom's age to the age of Mary, the sum is 62; but if you add the square of Mary's age to the age of Tom, the result is 176. What is the difference between in their ages?
Answer by ikleyn(52810) About Me  (Show Source):
You can put this solution on YOUR website!
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From the condition, we have these two equations


   T^2 + M  =   62     (1)

   T   + M^2 = 176     (2)



Subtract equation (1) from equation (2).   You will get


    (M^2 - T^2) + (T - M) = 176 - 62,   or

    (M+T)*(M-T) - (M-T)   = 114,   or

    (M - T)*(M + T - 1)   = 2*57 = 6*19.


So, there are two opportunities:  


    a)  M-T = 2,  M+T-1 = 57,  which implies  M = 29, T = 27,

or

    b)  M-T = 6,  M+T-1 = 19,  which implies  M = 13, T = 7,



Then the check with original equations (1) and (2)  leads to the UNIQUE


ANSWER.  The difference between their ages is 6 years.

Solved.