# Basic algebra: find break-even point

• 939
In summary, Mike needs to sell 4 shirts a day in order to break even and meet his goal of making a profit of $750 a day. This means he must charge$40.50 for each shirt in order to cover his fixed costs of $150 and the additional cost of$3 for each shirt.
939

Mike make shirts. He has fixed daily costs of $150. It costs an additional$3 to make each shirt. He would like to make a profit of $750 a day making shirts. If he can make 24 shirts a day, how much must he charge to meet his goal? Find break even point. ## Homework Equations c(x) = 3x + 150 p = r(x) - c(x) ## The Attempt at a Solution 1) p = r(x) - c(x) p = r(x) - c(24) 750 = r(x) - 222 750 = 972 - 222 972 = r(24) r = 40.5 r(x) = 40.5x He must charge$40.50.

2)40.5x = 3x + 150
37.5x = 150
x = 4

Break even point is $4 Last edited: It's not clear whether the last part means a break-even price or a break-even output. In your equations you've taken it to be break-even output, so the answer should be a number of shirts, not a number of dollars. And it's exact, not approximate. haruspex said: It's not clear whether the last part means a break-even price or a break-even output. In your equations you've taken it to be break-even output, so the answer should be a number of shirts, not a number of dollars. And it's exact, not approximate. Thanks. Btw, what if for a break even point, the "price" gives something approximate, i.e. 350.55 shirts for one and 350.71 for the other? Would you just take the break even point to be the first price that gives more revenue than cost? 939 said: Btw, what if for a break even point, the "price" gives something approximate, i.e. 350.55 shirts for one and 350.71 for the other? Would you just take the break even point to be the first price that gives more revenue than cost? Yes. The "break even point" is NOT a price. It is the number of shirts he must sell in order to just meet his costs. You assumed that yourself when you wrote "40.5x = 3x + 150".$40.50 is the price he is getting for each shirt. so 40.5x is the gross income if x is the number of shirts. Similarly, $3 is the marginal cost of each shirt so 3x is a cost only if x is the number of shirts. Your answer should be "He must make 4 shirts a day to break even", NOT "$4".

## 1. What is a break-even point in basic algebra?

A break-even point in basic algebra is the point at which the cost of producing a good or service is equal to the revenue generated by selling that good or service. In other words, it is the point at which there is no profit or loss.

## 2. How is the break-even point calculated?

The break-even point is calculated by dividing the fixed costs by the difference between the selling price and the variable cost per unit. This formula can be written as: Break-Even Point = Fixed Costs / (Selling Price - Variable Cost per Unit)

## 3. What is the importance of finding the break-even point?

Finding the break-even point is important for businesses because it helps them determine the minimum amount of sales needed to cover their costs. This information can then be used to make pricing and production decisions to ensure profitability.

## 4. Can the break-even point change over time?

Yes, the break-even point can change over time. Factors such as changes in production costs, selling price, and demand for the product or service can affect the break-even point.

## 5. How does understanding basic algebra help in finding the break-even point?

Understanding basic algebra is essential for finding the break-even point as it involves using mathematical equations to calculate the fixed costs, selling price, and variable cost per unit. Without a basic understanding of algebra, it would be difficult to accurately determine the break-even point.

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