Rafael is making punch and needs a gallon of raspberry sorbet and 2 liters of Sprite to make 12 cups. He pays $3.00 for a 2-liter container of Sprite 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? answer should be a dollar amount rounded to the nearest hundredth. and please explain
To make 12 cups of punch, Rafael needs 2 liters of Sprite. Since a gallon is equal to 3.785 liters, Rafael needs (2/3.785) * 1 gallon = 0.5286 gallons of raspberry sorbet.
Since there are 16 cups in a gallon, Rafael needs (0.5286 * 16) = 8.4576 cups of raspberry sorbet.
To make a $10 profit, Rafael needs to charge enough to cover his costs and add on to that.
The cost of the raspberry sorbet is $4.00 for 8.4576 cups, so the cost per cup is 4.00/8.4576 = $0.473.
The cost of the Sprite is $3.00 for 2 liters, which comes out to be (3.00/2) = $1.50 per liter or (1.50/3.785) = $0.40 per cup.
Therefore, the total cost per cup is $0.473 for the raspberry sorbet + $0.40 for the Sprite = $0.873 per cup.
If Rafael wants to make a $10 profit per 12 cups, he needs to charge enough to cover his costs and add the $10 profit.
Rafael should charge (0.873 * 12) + 10 = $20.28 for 12 cups of punch.
To find the minimum amount Rafael should charge per cup to make a $10 profit, divide the total price by the number of cups.
So the minimum amount Rafael should charge is 20.28/12 = $1.69 per cup.
Rounding this to the nearest hundredth, Rafael should charge $1.69 per cup to make a $10 profit.
are you 100% sure
I apologize for the error in my previous response. Let me recalculate the minimum amount Rafael should charge per cup to make a $10 profit.
Rafael needs 2 liters of Sprite, which costs $3.00, and 0.5286 gallons of raspberry sorbet, which cost $4.00 per quart. Since there are 4 quarts in a gallon, he needs (0.5286 * 4) = 2.1144 quarts of sorbet.
To convert quarts to cups, we multiply by 4. Therefore, Rafael needs (2.1144 * 4) = 8.4576 cups of raspberry sorbet.
The cost of the Sprite is $3.00 for 2 liters, which is equivalent to (3.00/2) = $1.50 per liter or (1.50/3.785) = $0.396 per cup.
The cost of the raspberry sorbet is $4.00 per quart, which is equivalent to (4.00/4) = $1.00 per cup.
Therefore, the total cost per cup is $1.00 for the raspberry sorbet + $0.396 for the Sprite = $1.396 per cup.
To make a $10 profit per 12 cups, Rafael needs to charge enough to cover his costs and add the $10 profit.
The total cost for 12 cups is (1.396 * 12) = $16.752.
If Rafael wants to make a $10 profit, he needs to charge (16.752 + 10) = $26.752 in total.
To find the minimum amount Rafael should charge per cup, divide the total price by the number of cups.
So the minimum amount Rafael should charge is 26.752/12 = $2.23 per cup.
Rounding this to the nearest hundredth, Rafael should charge $2.23 per cup to make a $10 profit.