Question

The sum of the digits of a two-digit number is equal to 15. If these digits switch places then you will get a number that is 27 less than the original number. Find these numbers.

Pls help :)

Answer 1

96, 69

Explanation:

We have a number with the digits (a, b):

a, b.

We can write the number as:

10a + b

If these digits switch places, we have:

10b + a

10b +a + 27 = 10a + b

9a - 9b = 27

9(a-b) = 27

(a-b) = 3

But we know that:

a + b = 15

Adding the equations:

(a+b) + (a-b) = 15 + 3

2a = 18

a = 9

a - b = 3

9 - b = 3

b = 6

The numbers are:

96

69