You spend $28 on ingredients to make cookies. You charge $4 per container of cookies. How many containers do you need to sell to earn $20 in profit?
To earn a profit of $20, you need to cover the cost of ingredients and achieve a profit margin of $20.
Let's calculate the profit margin per container:
Profit per container = Revenue per container - Cost per container
Since you charge $4 per container and spending $28 on ingredients, the cost per container is $28 / (number of containers).
Since we want a profit of $20, the equation becomes:
$20 = $4 * (number of containers) - $28/(number of containers)
On rearranging the equation, we get:
$20 + $28/(number of containers) = $4 * (number of containers)
Multiplying both sides by the number of containers, we have:
$20 * (number of containers) + $28 = $4 * (number of containers)^2
Rearranging the equation, we get:
$4 * (number of containers)^2 - $20 * (number of containers) - $28 = 0
This is a quadratic equation, and we can solve it by factoring, completing the square, or using the quadratic formula. However, it is evident from the equation that the number of containers must be a positive whole number.
So, by testing different positive whole number values for the number of containers, we can find the value that satisfies the equation:
Number of containers = 10
Therefore, you need to sell 10 containers of cookies to earn a profit of $20.
To find out how many containers of cookies you need to sell to earn a $20 profit, we need to determine the total cost of making the cookies and the selling price of each container of cookies.
1. Total cost of making the cookies:
Since you spent $28 on ingredients, the total cost of making the cookies is $28.
2. Selling price per container of cookies:
You charge $4 per container of cookies.
3. Profit per container:
To calculate the profit per container, subtract the total cost of making the cookies from the selling price per container:
Profit per container = Selling price per container - Total cost of making the cookies
Profit per container = $4 - $28 = -$24
4. Number of containers needed to earn $20 profit:
To earn a $20 profit, divide the desired profit by the profit per container and round it up to the nearest whole number:
Number of containers needed = Desired profit / Profit per container
Number of containers needed = $20 / (-$24) ≈ 0.8333
Since you cannot sell a fraction of a container, you would need to sell at least 1 container of cookies in order to earn a profit of $20.
To solve this problem, we need to break it down into steps:
Step 1: Calculate the cost of making one container of cookies
We are given that you spend $28 on ingredients to make cookies. Let's assume that you can make one container of cookies with these ingredients. Therefore, the cost of making one container of cookies is $28.
Step 2: Calculate the profit from selling one container of cookies
We are charging $4 per container of cookies. Since the cost of making one container is $28, the profit from selling one container of cookies is $4 - $28 = -$24.
Step 3: Determine the number of containers needed to earn a desired profit
We want to earn a profit of $20. To find out how many containers of cookies we need to sell to achieve this profit, we divide the desired profit by the profit from selling one container:
Number of containers needed = Desired profit / Profit from selling one container
Number of containers needed = $20 / -$24
Step 4: Calculate the number of containers needed
Divide the desired profit by the profit from selling one container:
Number of containers needed ≈ $20 / -$24 ≈ -0.8333
Since we can't sell a fraction of a container, we need to round up to the nearest whole number. Therefore, we need to sell at least 1 container of cookies to earn a profit of $20.