The sum of the two digits of a two-digit number is 15 and the difference between the two digits of the two digit number is 3. What is the product of the two digits of the two digit number?

Let the number be 10x + y where x > y
According to the question.
x + y = 15 ............(1)
and x - y = 3 .........(2)
Add the Equation (1) and (2) , We will get
x + y + x - y = 15 + 3
⇒ 2x = 18
⇒ x = 9
Put the value of x in equation (1). We will get
9 + y = 15
⇒ y = 15 - 9
⇒ y = 6
So we have digits of number x = 9, y = 6
∴ x * y = 9 * 6 = 54