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)
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To break even, Akeem's total costs must equal his total revenue.
Total costs = Cost per cup x Number of cups + Renter's fee
Total costs = $2 x Number of cups + $40
Total revenue = Selling price per cup x Number of cups
Total revenue = $6 x Number of cups
To break even, Total costs = Total revenue.
$2 x Number of cups + $40 = $6 x Number of cups
Simplifying the equation:
$40 = $6 x Number of cups - $2 x Number of cups
$40 = $4 x Number of cups
Dividing both sides by $4:
$40 / $4 = Number of cups
10 = Number of cups
Therefore, Akeem needs to sell 10 cups of lemonade to break even.
To find out how many cups Akeem needs to sell to break even, we need to determine the total cost and the total revenue.
First, let's calculate the total cost:
The cost to make each cup of lemonade is $2.
So, the cost to make 'x' cups of lemonade is 2x dollars.
Additionally, Akeem has to pay a $40 renter's fee for the stand.
Therefore, the total cost is the sum of the cost of making the lemonade and the renter's fee:
Total Cost = 2x + 40
Next, let's calculate the total revenue:
Akeem sells each cup of lemonade for $6.
So, the revenue from selling 'x' cups of lemonade is 6x dollars.
Now, to break even, the total revenue should equal the total cost:
Total Revenue = Total Cost
Substituting the expressions we found for the total cost and total revenue:
6x = 2x + 40
We need to solve the equation to find 'x'.
First, subtract 2x from both sides of the equation:
6x - 2x = 2x - 2x + 40
4x = 40
Then, divide both sides of the equation by 4 to isolate 'x':
4x/4 = 40/4
x = 10
So, Akeem needs to sell 10 cups of lemonade in order to break even.
Therefore, the answer is:
Akeem needs to sell 10 cups of lemonade to break even.