Question

Rafael 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? (Remember there are 4 quarts in a gallon.) Your answer should be a dollar amount rounded to the nearest hundredth.(1 point).

Answer 1

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.

1. Calculate the cost of raspberry sorbet:

   • A gallon is equal to 4 quarts.
   • The cost of a quart of sorbet is $4.00.
   • Therefore, the total cost for a gallon of sorbet is: $$4,\text{quarts}\times 4,\text{dollars/quart}=16,\text{dollars}$$

2. Calculate the cost of lemon-lime soda:

   • Rafael needs 2 liters of lemon-lime soda.
   • The cost of a 2-liter container is $3.00.
   • Thus, the total cost for the soda is: $$3,\text{dollars}$$

3. Calculate the total cost of the punch ingredients:

   • Total cost = Cost of sorbet + Cost of soda $$16,\text{dollars (sorbet)}+3,\text{dollars (soda)}=19,\text{dollars}$$

4. Add the desired profit:

   • Rafael wants to make a $10 profit.
   • Total profit needed = Total cost + Desired profit $$19,\text{dollars (total cost)}+10,\text{dollars (profit)}=29,\text{dollars}$$

5. Calculate the price per cup:

   • Rafael makes 12 cups of punch.
   • The minimum amount he should charge per cup is: $$\frac{29,\text{dollars}}{12,\text{cups}}\approx 2.4167,\text{dollars/cup}$$

6. Round to the nearest hundredth:

   • When rounded to the nearest hundredth, the price per cup is: $$2.42,\text{dollars}$$

Thus, the minimum amount Rafael should charge per cup of punch in order to make a $10 profit is $2.42.