A two-digit number is four times the sum of its digits. If 18 is added to the…

Step-by-Step Solution
Define the variables: Let the tens digit be x and the units digit be y. The two-digit number is represented as 10x + y.

Apply the first condition: "A two-digit number is four times the sum of its digits."

Equation: 10x + y = 4(x + y)

Simplify: 10x + y = 4x + 4y  =>  6x = 3y =>  y = 2x

Apply the second condition: "If 18 is added to the number, the digits reverse."

The reversed number is 10y + x.

Equation: (10x + y) + 18 = 10y + x

Simplify: 9x - 9y = -18  =>  y - x = 2

Solve the system of equations: Substitute y = 2x into y - x = 2.

2x - x = 2  =>  x = 2

y = 2(2)  =>  y = 4

Identify the number: With x = 2 and y = 4, the number (10x + y) is 24.