SOLUTION: It is an even two digit number . One half the number is 5 more than the number of days in a fortnight. the sum of the squares of the two digits is 73. what is it?

Let t = the tens digit
Let u = the units digit

The number = 10t + u

One half the number = (10t + u) = 5t + u

The number of days in a fortnight = 14

5 more than the number o days in a fortnight = 14+5 = 19

So

5t + u = 19

Multiplying through by 2 to clear of fractions:

10t + u = 38

We can stop right here because 10t + u IS the number,

so it's 38.

We didn't need to be given that, but we can check if we
like:

3² + 8² = 9 + 64 = 73.

Yes that's right, but we didn't need to be given that.  
We also didn't need to be given that it was even.

Answer: 38

Edwin