Final answer:
To solve this problem, assign variables to the digits of the two-digit number, form equations based on the given information, and solve the system of equations to find the number. The number is 42.
Step-by-step explanation:
To solve this problem, let's first assign variables to represent the tens and units digits of the two-digit number. Let the tens digit be x and the units digit be y.
From the given information, we know that the sum of the digits is 6, so we can write the equation x + y = 6.
We are also told that when 18 is subtracted from the number, the digits are reversed. This means that the original number can be expressed as 10x + y. So, when we subtract 18, we get 10x + y - 18. Since the digits are reversed, we can write the equation 10y + x = 10x + y - 18.
To solve this system of equations, we can use the substitution or elimination method. Solving the equations will give us the values of x and y, which will represent the tens and units digits of the number. The solution is x = 4 and y = 2. Therefore, the number is 42.