Akeem wants to have a lemonade stand at the community fair. It costs him $2 to make each cup of lemonade plus a $40 renter's fee for the stand. He sells the lemonade for $6 per cup. How many cups does Akeem have to sell to break even?
cups
To break even, Akeem's total costs need to be equal to his total revenue.
His costs include the cost to make each cup of lemonade ($2) multiplied by the number of cups sold (c) and the renter's fee for the stand ($40).
His revenue is the selling price per cup ($6) multiplied by the number of cups sold (c).
So the equation is:
2c + 40 = 6c
Subtracting 2c from both sides, we get:
40 = 4c
Dividing both sides by 4, we get:
c = 10
Therefore, Akeem needs to sell 10 cups of lemonade to break even.
To calculate the number of cups Akeem needs to sell to break even, we need to consider the costs and revenue involved.
1. First, let's calculate the total cost Akeem incurs for a cup of lemonade:
Cost per cup = cost of making each cup + stand renter's fee
Cost per cup = $2 + $40
Cost per cup = $42
2. Next, we'll calculate the selling price per cup of lemonade, which is $6.
3. To determine the break-even point, we'll divide the total costs by the selling price per cup:
Break-even point = Total costs / Selling price per cup
Break-even point = $42 / $6
Break-even point ≈ 7
Therefore, Akeem needs to sell at least 7 cups of lemonade to break even at the community fair.
To calculate the number of cups Akeem needs to sell to break even, we need to consider his expenses and revenue.
1. Calculate Akeem's expenses:
- The cost to make each cup of lemonade is $2.
- The renter's fee for the stand is $40.
Total expenses = (cost per cup * number of cups) + renter's fee
= (2 * x) + 40
= 2x + 40, where x is the number of cups.
2. Calculate Akeem's revenue:
- Akeem sells each cup of lemonade for $6.
Total revenue = price per cup * number of cups sold
= 6x, where x is the number of cups.
3. Find the break-even point:
The break-even point is when the total revenue equals the total expenses.
This can be represented by the equation:
Total revenue = Total expenses
6x = 2x + 40
We need to solve for x to find the number of cups:
6x - 2x = 40
4x = 40
x = 40 / 4
x = 10
Therefore, Akeem needs to sell 10 cups of lemonade to break even.