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?(1 point)
To break even, Akeem needs to earn back his initial investment of $40 plus the cost to make the lemonade, which is $2 per cup.
Let's call the number of cups he needs to sell "x".
His total earnings will equal his total costs:
6x = 2x + 40
Subtracting 2x from both sides, we get:
4x = 40
Dividing both sides by 4, we get:
x = 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 determine the total cost and total revenue.
1. Calculate the total cost:
- Cost per cup: $2
- Renter's fee: $40
Total cost = (Cost per cup × Number of cups) + Renter's fee
2. Calculate the total revenue:
- Selling price per cup: $6 per cup
Total revenue = Selling price per cup × Number of cups
3. Set the total cost equal to the total revenue and solve for the number of cups:
(Cost per cup × Number of cups) + Renter's fee = Selling price per cup × Number of cups
Now let's calculate the break-even point step-by-step:
(Cost per cup) × (Number of cups) + (Renter's fee) = (Selling price per cup) × (Number of cups)
2 × (Number of cups) + 40 = 6 × (Number of cups)
Simplify the equation:
2 × (Number of cups) + 40 = 6 × (Number of cups)
40 = 6 × (Number of cups) - 2 × (Number of cups)
40 = 4 × (Number of cups)
Divide both sides of the equation by 4:
40 / 4 = (Number of cups)
10 = (Number of cups)
Therefore, Akeem needs to sell 10 cups of lemonade to break even.
To determine how many cups Akeem needs to sell to break even, we need to calculate his total costs and then compare them to his total revenue.
Akeem's total costs include the cost to make each cup of lemonade, which is $2, and the renter's fee for the stand, which is $40. So, his total costs can be calculated as follows:
Total costs = (Cost per cup * Number of cups) + Renter's fee
= ($2 * Number of cups) + $40
Akeem's total revenue will be the selling price per cup multiplied by the number of cups he sells. Given that he sells each cup for $6, his total revenue can be calculated as follows:
Total revenue = Selling price per cup * Number of cups
= $6 * Number of cups
Now, to find the breakeven point, we need to set the total costs equal to the total revenue and solve for the number of cups:
Total costs = Total revenue
($2 * Number of cups) + $40 = $6 * Number of cups
Simplifying the equation:
$40 = $4 * Number of cups
Now, we can solve for the number of cups by dividing both sides of the equation by $4:
Number of cups = $40 / $4
= 10 cups
Therefore, Akeem needs to sell 10 cups of lemonade to break even.