Question 467728
Let's call that number x. We need to convert the word problem to an equation. Recall that ratio means a fraction. 3 times that number is going to be 3x. The ratio of 3x and 5 is the fraction 3x/5. This is equal to the difference between that number x and 2. In other words, 

3x/5 = x-2 

Now we can solve a simple algebra problem. Multiply both sides by 5. 

3x = 5x - 10 

Now it is easy to solve. Add 10 to both sides to get 

3x + 10 = 5x 

Subtracting 3x from both sides gives 
10 = 2x 

Finally dividing by 2 gives x = 5. 

Now we can check. The ratio of 3 times that number (which is 15) and 5 is 15/5 = 3. The difference between that number (5) and 2 is also 3, so it works!