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?
To make 12 cups of punch, Rafael needs 12 cups * 1 gallon / 16 cups/gallon = <<12*1/16=0.75>>0.75 gallons of raspberry sorbet.
He needs 2 liters * 1 gallon/3.78541 liters = <<2*1/3.78541=0.52834>>0.52834 gallons of Sprite.
Therefore, the total volume of liquid in the punch is 0.75 gallons + 0.52834 gallons = <<0.75+0.52834=1.27834>>1.27834 gallons.
Thus, Rafael is making 1.27834 gallons * 16 cups/gallon = <<1.27834*16=20.45344>>20.45344 cups of punch.
The raspberry sorbet costs $4.00/quart * 1 quart/4 cups * 20.45344 cups = $20.45.
The Sprite costs $3.00/2 liters * 2 liters/67.6280451 ounces * 33.8140226 ounces/liter * 20.45344 cups = $20.45.
Thus, the total cost is $20.45 + $20.45 = $<<20.45+20.45=40.90>>40.90.
Rafael wants to make a $10 profit, so he should charge $40.90 + $10 = $<<40.90+10=50.90>>50.90.
Since there are 12 cups of punch, Rafael should charge $50.90 / 12 cups = $<<50.90/12=4.24>>4.24 per cup. Answer: \boxed{4.24}.
To find the minimum amount Rafael should charge per cup of punch, we need to calculate the cost of making the punch and then add the desired profit.
Step 1: Convert the measurements to a common unit.
- 1 gallon is equal to 3.785 liters.
- 1 quart is equal to 0.946 liters.
- So, Rafael needs 3.785 liters of raspberry sorbet and 2 liters of Sprite to make 12 cups.
Step 2: Calculate the cost of the ingredients.
- Rafael pays $4.00 for a quart of sorbet, which is 0.946 liters.
- So, the cost of 3.785 liters of sorbet is (4.00 * 3.785) = $15.14.
- Rafael pays $3.00 for a 2-liter container of Sprite.
- So, the cost of 2 liters of Sprite is $3.00.
Step 3: Calculate the total cost of making the punch.
- The total cost is the sum of the sorbet cost and the Sprite cost.
- So, the total cost is ($15.14 + $3.00) = $18.14.
Step 4: Calculate the cost per cup of punch.
- Since Rafael makes 12 cups, the cost per cup is ($18.14 / 12) = $1.51.
Step 5: Calculate the minimum amount to charge per cup to make a $10 profit.
- The desired profit is $10.00.
- So, the minimum amount to charge per cup is ($1.51 + $10.00) = $11.51.
Therefore, Rafael should charge at least $11.51 per cup of punch to make a $10 profit.
To determine the minimum amount Rafael should charge per cup of punch to make a $10 profit, we first need to calculate the total cost of the ingredients required to make 12 cups of punch.
1. Calculate the cost of 2 liters of Sprite:
- Rafael paid $3.00 for a 2-liter container of Sprite.
- Since he needs 2 liters to make 12 cups, we divide $3.00 by 2 to get the cost per liter: $3.00 / 2 = $1.50.
- Therefore, he spends $1.50 on Sprite to make 12 cups.
2. Calculate the cost of a gallon of raspberry sorbet:
- Rafael paid $4.00 for a quart of sorbet.
- Since there are 4 quarts in a gallon, we multiply $4.00 by 4 to get the cost of a gallon: $4.00 * 4 = $16.00.
- Therefore, he spends $16.00 on raspberry sorbet to make 12 cups.
3. Calculate the total cost of ingredients:
- Add the cost of Sprite ($1.50) and the cost of raspberry sorbet ($16.00): $1.50 + $16.00 = $17.50.
- Therefore, Rafael spends $17.50 on ingredients to make 12 cups of punch.
4. Calculate the cost per cup:
- Divide the total cost of ingredients ($17.50) by the number of cups (12): $17.50 / 12 = $1.46 (rounded to two decimal places).
- Therefore, Rafael's cost per cup of punch is $1.46.
5. Calculate the minimum amount to charge for a $10 profit:
- Add the cost per cup ($1.46) to the desired profit ($10.00): $1.46 + $10.00 = $11.46.
- Therefore, the minimum amount he should charge per cup of punch to make a $10 profit is $11.46.
Note: Depending on the pricing strategy, Rafael might choose to round up this price to the nearest convenient value to avoid dealing with small change.