Calculating Total Cost with Variable n: C = 7500 + 8n

[Guic]

C = 7500 + 8n

 

[HallsofIvy]

Okay, the title said "solution" and that's the solution! But to what problem?

Or is that a "problem" itself and not a "solution"? That is, is the problem (strictly speaking an equation alone is not a "problem") to solve that equation for n? If so it would have been a good idea to tell us that!

Given C= 7500+ 8n, we want to "solve for n". To solve for an unknown means to get it by itself on one side of the equation. That is, we want "n= something".

The first thing we might do is use the fact that "A= B" is the same as "B= A" to write 7500+ 8n= C. Now, "n" is not alone because two things have been done to it: it has been multiplied by 8 and then 7500 is added to it. To get n by itself, we must "undo" those things. That is, instead of "first multiply by 8 then add 7500" (which is what "7500+ 8n" means) we do the opposite of each step (the opposite of "multiply by 8" is "divide by 8 and the opposite of "add 7500" is "subtract 7500". We must do those in the opposite order and, of course, what ever we do to one side of an equation we must do to the other side.

We have 7500+ 8n= C and we "subtract 7500" from both sides to get
7500+ 8n- 7500= 8n= C- 7500

Then we divide both sides by 8: n= (C- 7500)/8.
Notice the parentheses! We need to divide the entire right side, C- 7500, by 8. If we wrote "C- 7500/8" that would mean we were just dividing 7500 by 8.