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 needs to cover his costs, which include the cost to make each cup of lemonade and the stand's rental fee.
The total cost per cup can be calculated by adding the cost to make each cup of lemonade ($2) to the rental fee for the stand ($40):
Total cost per cup = Cost to make each cup + Rental fee for stand
= $2 + $40
= $42
To break even, Akeem needs to sell enough cups to cover the total cost per cup ($42).
Therefore, Akeem needs to sell the cups for $42 / $6 per cup, which equals 7 cups.
So, Akeem needs to sell 7 cups to break even. Answer: \boxed{7}.
To calculate the number of cups Akeem needs to sell to break even, you need to consider his costs and revenue.
First, let's calculate the total cost for Akeem. Each cup of lemonade costs $2 to make, and he also has a $40 rental fee for the stand. So the total cost for Akeem is $2 per cup + $40 in rental fees.
Total Cost = ($2 per cup) + ($40 rental fee)
Next, let's calculate the revenue per cup for Akeem. He sells each cup for $6.
Revenue per cup = $6
To break even, Akeem's total revenue needs to equal his total cost. Therefore, we can set up the equation:
Total Revenue = Total Cost
Now, let's substitute the values into the equation:
Revenue per cup x Number of cups = Cost per cup x Number of cups + Rental fee
$6 x Number of cups = $2 x Number of cups + $40
Simplifying the equation:
6c = 2c + 40
Combining like terms:
6c - 2c = 40
4c = 40
Dividing each side by 4:
c = 10
Therefore, Akeem needs to sell 10 cups of lemonade to break even.
To determine the number of cups Akeem needs to sell to break even, we need to consider his expenses and revenue.
Expenses:
- Cost to make each cup of lemonade: $2
- Renter's fee for the stand: $40
Total expenses per cup sold:
$2 (cost to make) + ($40 / number of cups sold)
Revenue:
- Selling price for each cup of lemonade: $6
To break even, Akeem's revenue must cover his expenses. Mathematically, this can be expressed as:
Revenue = Total Expenses
Using the values we have:
$6 (revenue per cup) * number of cups sold = $2 (cost to make) * number of cups sold + ($40 / number of cups sold)
To solve this equation, we can start by simplifying it:
6n = 2n + (40 / n)
To combine like terms, move the 2n term to the left side:
6n - 2n = 40 / n
Simplifying further:
4n = 40 / n
To remove the fraction, multiply both sides by n:
4n^2 = 40
Now, divide both sides by 4 to isolate n:
n^2 = 10
Taking the square root of both sides:
n = √10
Therefore, Akeem needs to sell approximately √10 cups of lemonade to break even.