Year 9 Maths

Question

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.
a) How old is Malcolm if the sum of 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?

Answer 1

If the son's age is  xy  =  10x + y

Mom's age is yx = 10y + x

 

Mother is 27 years older than Malcolm:

10x + y + 27 = 10y + x

9x - 9y = -27

x-y = -3

 

Your possibilities are:

14, 41

25, 52

36, 63

47, 74

58, 85

69, 96

 

a)  The sum of the digits in Malcolm's age is 5

     Malcolm is 14, mother is 41

 

b)  The relationship between the digits in Malcolm's age is

     x - y = -3

 

c)  6 ages:  14, 25, 36, 47, 58, 69