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?
The cost to make one cup of lemonade is $2.
The renter's fee is $40.
Therefore, the total cost to set up the lemonade stand is $2 x N + $40, where N is the number of cups he sells.
The price he sells each cup for is $6.
To break even, the total revenue from selling N cups of lemonade must equal the total cost, so $6 x N = $2 x N + $40.
Combining like terms on the right side gives $6N = $2N + $40.
Subtracting $2N from both sides gives $4N = $40.
Dividing both sides by $4 gives N = 10.
Therefore, Akeem must sell 10 cups of lemonade to break even. Answer: \boxed{10}.
To determine the number of cups Akeem needs to sell to break even, we need to consider the total costs and the selling price of each cup.
1. Calculate Akeem's total costs:
- Cost per cup: $2
- Renter's fee for the stand: $40
- Total costs = Cost per cup + Renter's fee = $2 + $40 = $42
2. Calculate the selling price per cup: $6
3. Determine the contribution margin per cup:
- Contribution margin = Selling price - Cost per cup = $6 - $2 = $4
4. Determine the breakeven point:
- Breakeven point = Total costs / Contribution margin = $42 / $4 = 10.5 cups
Since Akeem cannot sell a fractional cup, he needs to sell at least 11 cups to break even.
To determine how many cups Akeem needs to sell to break even, we need to calculate his total costs and compare them to his total revenue.
Akeem's cost per cup is $2. He also has a renter's fee of $40 for the stand. To calculate his total costs, we multiply the cost per cup by the number of cups he needs to sell, and then add the renter's fee:
Total Costs = (Cost per cup × Number of cups) + Renter's fee
Let's assume Akeem needs to sell x cups to break even. The equation becomes:
Total Costs = ($2 × x) + $40
Akeem sells each cup for $6. To calculate his total revenue, we multiply the selling price per cup by the number of cups:
Total Revenue = Selling Price per cup × Number of cups
Since Akeem wants to break even, his total revenue should be equal to his total costs:
Total Revenue = Total Costs
Setting the equations equal to each other:
($6 × x) = ($2 × x) + $40
Now, we can solve the equation to find the value of x, which represents the number of cups Akeem needs to sell to break even:
6x = 2x + 40
Rearranging the equation:
6x - 2x = 40
4x = 40
Dividing both sides of the equation by 4:
x = 40 ÷ 4
x = 10
Therefore, Akeem needs to sell 10 cups of lemonade to break even at the community fair.