Question 1134351
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The difference between the squares of consecutive integers is equal to the sum of the two integers:<br>
5^2-4^2 = 25-16 = 9 = 5+4
13^2-12^2 = 169-144 = 25 = 13+12
(n+1)^2-n^2 = (n^2+2n+1)-n^2 = 2n+1 = (n+1)+n<br>
Since you know their ages are consecutive integers, the difference of the squares of their ages is the sum of their two ages.  Since the sum of their ages is 97 and their ages are consecutive integers, their ages are 49 and 48.