The mean of a set of data is 45 years. find the missing numbers in the data set 40, 45, 48, ? 54, ? 45. explain the method or strategy you used

If the number is missing, it's safe to say we can turn it into a variable, because it is unknown. We'll call this variable u, which stands for "unknown". Now, think about this: Mean is all of the values added together divided the amount of values. We'll need to work backwards to find the number. To better see how, write out what we know so far:

(40 + 45 + 48 + u + 54)/5= 45. Why are we dividing by 5? Because there are 5 values you need to add together :)

     Now what? Well, now, it's like a normal equation! Just solve for the variable "u"! :) First, combine like terms. Add all of the numbers you know together. You should get this:

(187+u)/5=45
     What do you do first? Ask the order of operations! Order of operations says multiplication and division come before addition and subtraction, so we have to get rid of that /5 in the equation. How do we do this? We use inverse operations. What's the opposite of division? Multiplication! However, whatever you do to one side of the equation, you must do to the other. Multiply both sides by 5. ((187+u)/5)*5... Do you see how the /5 and the *5 cancel out? On that side, you're left with 187+u. For the other side, =45, you also need to multiply by 5. 45*5=225. 
     Now, you're left with 187 + u = 225. What next? This is a basic equation; subtract 187 from both sides; 187-187 is 0, and 225 - 187 is 38. 0 + u =38 is what you get. Of course, that's just u=38.  Wait didn't "u" stand for "unknown"? That means that 38 is your missing value! You've found the answer!