THEIR AGES 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 age of Tom, the result is 176. Can you say
what are the ages of Tom and Mary?

Tom’s age is 7 years

Mary’s age is 13 years

Step-by-step explanation:

Since we do not know the ages, let’s represent the ages by variables at first.

Let m represent mary’s age will t represent Tom’s age.

Now, let’s proceed to have equations.

Adding square of Tom’s age (t^2) to mary’s age give 62

t^2 + m = 62 •••••••(i)

Adding square of mary’s age (m^2) to Tom’s age give 176

m^2 + t = 176 •••••••(ii)

Now, to get the individual ages, we will need to solve both equations simultaneously.

Solving both equations simultaneously without mathematical softwares can be a little hard.

By the use of mathematical software ( wolfram alpha to be specific), we can input both equations and allow the software to solve.

By inputing these equations, we have the values of t to be 7 and m to be 13

And if we try to check by inspection, we can see that these values are actually correct.

7^2 + 13 = 62

13^2 + 7 = 176