Malcolm’s mother is 27 years older than he is and their ages are both two digit numbers. If Malcolm swaps the digits in his age he gets his mother’s age.

Question

a) How old is Malcolm if the sum o the digits in his age is 5?
b) What is the relationship between the digits in Malcolm’s age if the sum of the digits is unknown.
c) If the sum of the digits in Malcolm’s two-digit age is unknown, how many possible ages could he be? What are these ages?

All the solution has to be in algebraic form

Answer 1

a: d+u=5
10(5-u)+u+27=10u+(5-u)
u=4
d=1
he is 14
b:9d+27=9u
c:from 14,25,.. to 69