Question

The sum of the digits of a 2-digit number is 14. The number obtained by interchanging the digits is 36 more than the given number. Find the number.

Answer 1

By setting up a system of linear equations based on the given conditions about the sum of the digits and the result of interchanging the digits, we deduce that the two-digit number in question is 59.

Step-by-step explanation:

Finding a Two-Digit Number Based on Given Conditions

Let us denote the two-digit number as 10x + y where x is the tens digit and y is the ones digit. According to the question, the sum of the digits of a two-digit number is 14, which gives us the equation:

x + y = 14 (1)

The number obtained by interchanging the digits is 36 more than the given number, leading to the equation:

10y + x = 10x + y + 36 (2)

Subtract equation (1) from equation (2), we get:

9y - 9x = 36

y - x = 4 (3)

Now we have a system of linear equations:

1. x + y = 14
2. y - x = 4

Adding both equations, we get:

2y = 18

y = 9

Substituting y back into equation (1):

x = 14 - 9

x = 5

Thus, the two-digit number is 59.