Rafael is making punch and needs a gallon of raspberry sorbet and 2 litters of lemon-lime soda to make 12 cups. He pays $3.00 for a 2-litter container of lemon-lime soda and $4.00 for a quart of sorbet. What is the minimum amount he should charge per cup of punch to make a 10 dollar profit? The answer should be a dollar amount rounded to the nearest 100th.
To find out the minimum amount Rafael should charge per cup of punch to make a $10 profit, we need to calculate his total cost and then determine how many cups he needs to sell to cover that cost plus the desired profit.
First, let's calculate Rafael's total cost:
- 1 gallon of raspberry sorbet is approximately equal to 4 quarts, so Rafael needs 4 quarts of sorbet for 12 cups of punch. Since he pays $4.00 for a quart of sorbet, his total cost for sorbet is 4 * $4.00 = $16.00.
- Rafael needs 2 liters of lemon-lime soda for 12 cups of punch. He pays $3.00 for a 2-liter container, so his total cost for soda is $3.00.
Next, let's determine the total cost for Rafael:
Total Cost = Cost for Sorbet + Cost for Soda
Total Cost = $16.00 + $3.00 = $19.00
Now, we need to calculate how much Rafael needs to charge per cup to make a $10 profit:
Desired Profit = Total Revenue - Total Cost
$10.00 = (Price per Cup * Number of Cups) - $19.00
$10.00 + $19.00 = (Price per Cup * Number of Cups)
$29.00 = Price per Cup * Number of Cups
Since Rafael wants to make a profit of $10 and we already know the total cost is $19.00, Rafael needs to cover the $29.00 - $19.00 = $10.00 profit by selling a certain number of cups.
To calculate the number of cups Rafael needs to sell, we need to consider that he has 12 cups in total. Therefore, the equation becomes:
$29.00 = Price per Cup * 12
Now, let's solve for the Price per Cup:
Price per Cup = $29.00 / 12
Price per Cup = $2.42 (rounded to the nearest 100th)
Therefore, to make a $10 profit, Rafael should charge a minimum of $2.42 per cup of punch (rounded to the nearest 100th).
To determine the minimum amount Rafael should charge per cup of punch, we need to calculate the total cost of the ingredients and then add the desired $10.00 profit.
The punch recipe requires a gallon of raspberry sorbet and 2 liters of lemon-lime soda to make 12 cups.
First, let's calculate the cost of the sorbet:
Rafael pays $4.00 for a quart of sorbet, and there are 4 quarts in a gallon. So, the cost of a gallon of sorbet is:
4 quarts/gallon * $4.00/quart = $16.00/gallon.
Next, let's calculate the cost of the lemon-lime soda:
Rafael pays $3.00 for a 2-liter container of soda.
To convert liters to gallons:
1 liter ≈ 0.264172 gallons.
So, 2 liters of soda is approximately 0.528344 gallons.
Therefore, the cost of the lemon-lime soda is (approximately):
0.528344 gallons * $3.00/gallon = $1.59.
Now, let's calculate the total cost of the ingredients:
Cost of sorbet + Cost of soda = $16.00 + $1.59 = $17.59.
To determine the minimum amount Rafael should charge per cup to make a $10.00 profit, we divide the total cost by the number of cups:
Total cost / 12 cups = $17.59 / 12 = $1.46 (rounded to the nearest 100th).
Finally, to cover the $10.00 profit, we add it to the cost per cup:
$1.46 + $10.00 = $11.46.
Therefore, Rafael should charge approximately $11.46 per cup of punch to make a $10.00 profit.
Wrong answer
Apologies for the mistake. Let's recalculate the minimum amount Rafael should charge per cup of punch.
The total cost of ingredients for 12 cups of punch is the cost of the sorbet and soda combined:
Cost of sorbet: $4.00 per quart
Rafael needs 1 gallon (4 quarts) of sorbet, so the cost of sorbet is 4 * $4.00 = $16.00
Cost of soda: $3.00 for 2 liters
Rafael needs 2 liters of soda, so the cost of soda is $3.00
Total cost of ingredients: $16.00 + $3.00 = $19.00
To make a $10.00 profit, Rafael needs to cover his total cost ($19.00) plus the desired profit ($10.00) for a total revenue of $19.00 + $10.00 = $29.00
Since Rafael wants to make a profit and cover his costs for 12 cups, the minimum amount he should charge per cup is $29.00 / 12 cups = $2.42 (rounded to the nearest 100th).
Therefore, Rafael should charge at least $2.42 per cup of punch to make a $10.00 profit.
To make 12 cups of punch, Rafael needs 1 gallon (4 quarts) of sorbet and 2 liters (67.63 ounces) of lemon-lime soda.
Since 1 gallon is equal to 128 ounces, Rafael needs 128/12 = 10.67 ounces of sorbet per cup of punch.
To charge the minimum amount per cup of punch, Rafael needs to divide the total cost by the number of cups.
The cost of 10.67 ounces of sorbet is 10.67/8 * $4.00 = $5.34.
The cost of 67.63 ounces of lemon-lime soda is 67.63/33.8 * $3.00 = $6.06.
The total cost of ingredients per cup of punch is $5.34 + $6.06 = $11.40.
To make a $10.00 profit, Rafael needs to charge $11.40 + $10.00 = $21.40.
Therefore, Rafael should charge $21.40 per cup of punch to make a $10.00 profit.