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

• MHB
• Guic
In summary, the conversation discusses how to solve the equation C= 7500+ 8n for n. The first step is to use the fact that "A= B" is the same as "B= A" to write 7500+ 8n= C. Then, to get n by itself, the steps of multiplying by 8 and adding 7500 must be undone in the opposite order. This is done by subtracting 7500 from both sides and then dividing both sides by 8. The final solution is n= (C- 7500)/8.
Guic
C = 7500 + 8n

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.

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## 1. How do you calculate the total cost using the formula C = 7500 + 8n?

To calculate the total cost, you simply need to plug in the value of n into the formula and solve for C. For example, if n = 10, the total cost would be calculated as C = 7500 + 8(10) = 7500 + 80 = 7580.

## 2. What does the number 7500 represent in the formula C = 7500 + 8n?

The number 7500 represents the fixed cost or the cost that remains constant regardless of the value of n. This could include expenses such as rent, insurance, or equipment costs.

## 3. What does the number 8 represent in the formula C = 7500 + 8n?

The number 8 represents the variable cost per unit. This means that for every unit of n, there will be an additional cost of 8. This could include expenses such as materials or labor costs.

## 4. Can this formula be used for any type of cost calculation?

This formula can be used for calculating total cost in situations where there is a fixed cost component and a variable cost component. However, it may not be applicable for all types of cost calculations, such as those with multiple variables or non-linear relationships.

## 5. How can this formula be applied in a real-world scenario?

This formula can be applied in various real-world scenarios, such as calculating the total cost of producing a certain number of products, determining the cost of a service based on the number of hours worked, or estimating the total cost of a project with a fixed budget and variable expenses.

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