Raphael is making punch and needs a gallon of raspberry sorbet and 2 liters of lemon-lime soda to make 12 cups. He pays $3.00 for a 2 liter 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 profit?
First find the number of liters in 12 cups: 12 cups * 1 liter / 4 cups = <<12*1/4=3>>3 liters
Then divide the total cost of the soda by the number of liters to find the cost per liter: $3.00 / 2 liters = $<<3/2=1.50>>1.50/liter
Multiply the number of liters by the cost per liter to find the total cost of the soda: 3 liters * $1.50/liter = $<<3*1.5=4.50>>4.50
Then multiply the cost per quart of sorbet by the number of quarts to find the total cost of the sorbet: $4.00/quart * 1 gallon/4 quarts = $<<4*1/4=1>>1.00
Then add the cost of the soda and sorbet to find the total cost: $4.50 + $1.00 = $<<4.5+1=5.50>>5.50
Then add the desired profit to find the total price he should charge: $10.00 + $5.50 = $<<10+5.5=15.50>>15.50
Finally, divide the total price by the number of cups to find the price per cup: $15.50 / 12 cups = $<<15.5/12=1.29>>1.29. Answer: \boxed{1.29}.
To determine the minimum amount Raphael should charge per cup of punch to make a $10 profit, we need to calculate the cost per cup and add the desired profit.
1. Calculate the total cost of the ingredients:
- Raspberry sorbet: Raphael needs a gallon, which is 4 quarts. Therefore, he will need 4 * $4.00 = $16.00 worth of sorbet.
- Lemon-lime soda: Raphael needs 2 liters, which is approximately 2.113 quarts. Therefore, he will need 2.113 * ($3.00/2) = $3.17 worth of soda.
- Total cost of ingredients: $16.00 (sorbet) + $3.17 (soda) = $19.17.
2. Determine the number of cups Raphael can make with the ingredients:
- Assuming one cup equals 12 cups, then Raphael can make 12 cups of punch.
3. Calculate the cost per cup of punch:
- Cost per cup = Total cost of ingredients / Number of cups
- Cost per cup = $19.17 / 12 cups = $1.60 per cup.
4. Add the desired profit of $10.00:
- Minimum price per cup = Cost per cup + Desired profit
- Minimum price per cup = $1.60 + $10.00 = $11.60.
Therefore, Raphael should charge a minimum of $11.60 per cup of punch to make a $10.00 profit.
To find the minimum amount Raphael should charge per cup of punch to make a $10 profit, we need to calculate the total cost of the ingredients and then add the desired profit.
First, let's calculate the total cost of the ingredients.
Raspberry sorbet is sold in quarts, and Raphael needs a gallon of sorbet. Since there are 4 quarts in a gallon, Raphael would need to buy 4 quarts of sorbet. Since each quart of sorbet costs $4.00, the total cost of the sorbet is 4 * $4.00 = $16.00.
Raphael needs 2 liters of lemon-lime soda, and he pays $3.00 for a 2-liter container. Therefore, the total cost of the lemon-lime soda is $3.00.
Next, we add the cost of the sorbet and soda to get the total cost of the ingredients: $16.00 + $3.00 = $19.00.
To make a $10 profit, Raphael needs to include this in the total price.
Therefore, the minimum amount he should charge per cup of punch to make a $10 profit is ($19.00 + $10.00) divided by the number of cups (12).
($19.00 + $10.00) / 12 = $29.00 / 12
Calculating this, we find that Raphael should charge approximately $2.42 per cup of punch to make a $10 profit.