Question

The sum of the digits of a two-digit number is 11. when the digits are reversed, the number increases by 27. find the original number.

Answer 1

The sum of the digits of a two-digit number is 11. when the digits are reversed, the number increases by 27. find the original number.

Answer 2

The original number is 4 and 7

Let the unknown numbers be x and y

If the sum of the digits of a two-digit number is 11, hence;

• x + y = 11
• x = 11 - y ,........................... 1

If the digits are reversed and increased by 27, this is expressed as:

• 10y + x = 10x + y + 27 ........................2

Substitute equation 1 into 2 to have:

10y + x = 10x + y + 27

10y + 11 - y = 10(11-y) + y + 27

9y + 11 = 110-10y + y + 27

9y + 11 = 137 - 9y

9y + 9y = 137 - 11

18y = 126

y = 126/18

y = 7

Recall that x + y = 11

x = 11 - y

x = 11 - 7

x = 4

This shows that the original number is 4 and 7

Learn more about simultaneous equations: https://brainly.com/question/21654746