Daily Mail Mindbender

[Gavmacp]

Could someone explain how you would tackle this question I.e. the mathematics in finding the solution. I know the answer as solution is provided.
If you reverse the two digits of Alec's age, add 17 and divide by two, you'll have Alec's age. How old is Alec today?

[Fibonacci]

Alex's age: xy - the value of this can be written as 10x+y
reverse the digits yx - the value of this can be written as 10y+x
Now
(10y+x+17) / 2 = 10x + y
so
10y + x +17 = 20x +2y
this can be rearranged to give
19x - 8y = 17
so looking for mutiples of 19 and 8 which differ by 17
57 & 40
57 = 19x so x=3
40 = 8x so y =5
Alec's age - 35
check
reverse 35 - 53
53+ 17 =70
70 / 2 = 35

[maurice]

He is 35 (found by trial & error)!

[ginger1945]

Alec's age 10a + b which = (10b + a +17)/2
simplify 19a - 8b = 17
a = 17/19 + 8b/19
as dealing with whole numbers we need to find "b" that leaves remainder 2/19 which will make 17/19 whole ie b = 5 and a then equals 3
(congruences and mod maths also solve)