How to solve this?

Question

3. Brendan was born on his grandmother’s birthday. The two digits of Brendan’s age today are the reverse of the digits of his grandmother’s age. The grandmother’s age is a prime number. Ten years from now, his grandmother will be three times as old as Brendan will be then. How old are Brendan and his grandmother?

Answer 1

Hi Sunay,

 

Let

B = Brendan's age

G = Grandmother's age

We know G is prime

We know the two digits of Brendan's age are the reverse of the two digits of Grandma's age

Finally

G+10 = 3(B+10)

G = 3B +20

 

Since Grandma's age is a prime number and it's a two-digit number, it can be.

11,13,17,19,23,29,31,37,41,43,47,53,59,61,67,71,73,79,83,89,97

 

But Grandma's age must contain digits where the ones digit < tens digit or Brendan will be older than his grandmother.

So our possible Grandma ages reduces to

31,41,43,53,61,71,73,83,97

 

Now let's test these ages in the formula G = 3B + 20

The only one that works is

G = 71

This would mean B = 17

3(17) + 20 = 71