Question

number sense the sum of the digits of a two - digit number is 8. when the digits are reversed, the number increases by 36. find the original number. the original number is \square.

Explanation:

Step1: Define variables for digits

Let the tens digit be \( x \) and the units digit be \( y \). The original number is \( 10x + y \), and the reversed number is \( 10y + x \).

Step2: Set up first equation from digit sum

The sum of the digits is 8, so \( x + y = 8 \).

Step3: Set up second equation from number increase

When reversed, the number increases by 36: \( (10y + x) - (10x + y) = 36 \). Simplify this: \( 10y + x - 10x - y = 36 \) → \( 9y - 9x = 36 \) → Divide by 9: \( y - x = 4 \).

Step4: Solve the system of equations

We have:

1. \( x + y = 8 \)
2. \( y - x = 4 \)

Add the two equations: \( (x + y) + (y - x) = 8 + 4 \) → \( 2y = 12 \) → \( y = 6 \).

Substitute \( y = 6 \) into \( x + y = 8 \): \( x + 6 = 8 \) → \( x = 2 \).

Step5: Find the original number

Original number is \( 10x + y = 10(2) + 6 = 26 \).

Answer:

26