Final answer:
To find the two-digit number, we set up an equation using the given information and solve for the digits. The answer is 42.
Step-by-step explanation:
To solve this problem, we can start by setting up the equation. Let the tens digit of the two-digit number be x and the units digit be y. The given information tells us that xy = 8. We can also express the number as 10x + y. When 18 is subtracted from the number, the digits interchange their places, so we have the equation 10x + y - 18 = 10y + x.
Simplifying the equation, we get 9x - 9y = 18. Since 9 is a common factor, we can divide both sides of the equation by 9 to get x - y = 2.
Now, we can solve for x and y by trying different values that satisfy the equation x - y = 2. The only solution that works is x = 4 and y = 2. Therefore, the two-digit number is 42.