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)
Rafael needs a gallon of raspberry sorbet, which is equal to 4 quarts. So he needs 4 quarts * $4.00/quart = $<<4*4=16.00>>16.00 of sorbet.
He also needs 2 liters of lemon-lime soda, which costs $3.00 per 2-liter container. So he needs 1 container * $3.00/container = $<<1*3=3.00>>3.00 of soda.
In total, Rafael spends $16.00 + $3.00 = $<<16+3=19.00>>19.00 on ingredients.
To make a $10.00 profit, Rafael must charge at least $19.00 + $10.00 = $<<19+10=29.00>>29.00 in total.
Since there are 12 cups, each cup should be priced at $29.00 / 12 cups = $<<29/12=2.42>>2.42 per cup.
Rounded to the nearest hundredth, Rafael should charge $2.42 per cup of punch. Answer: \boxed{2.42}.
To find the minimum amount Rafael should charge per cup of punch, we need to calculate the total cost and the total revenue.
First, let's calculate the total cost:
- Rafael needs a gallon of raspberry sorbet, which is equal to 4 quarts. Since he pays $4.00 for a quart, the total cost of sorbet is 4 quarts * $4.00/quart = $16.00.
- Rafael needs 2 liters of lemon-lime soda, and he pays $3.00 for a 2-liter container. So, the total cost of soda is $3.00.
The total cost of ingredients is $16.00 + $3.00 = $19.00.
Next, let's calculate the revenue:
Rafael is making 12 cups of punch. To make a $10 profit, he needs to charge an amount that covers the total cost of $19.00 plus the $10.00 profit.
Total revenue = Total cost + Profit
Total revenue = $19.00 + $10.00 = $29.00
To find the minimum amount he should charge per cup, we divide the total revenue by the number of cups:
Minimum amount charged per cup = Total revenue / Number of cups
Minimum amount charged per cup = $29.00 / 12 cups = $2.41666666667
Rounding this value to the nearest hundredth, the minimum amount Rafael should charge per cup of punch to make a $10 profit is $2.42.
First, we need to calculate how much the gallon of raspberry sorbet costs. Since there are 4 quarts in a gallon, and Rafael pays $4.00 for a quart of sorbet, the total cost of a gallon of sorbet would be 4 x $4.00 = $16.00.
Next, we need to calculate the total cost of the lemon-lime soda. Rafael pays $3.00 for a 2-liter container of soda, and since he needs 2 liters of soda to make 12 cups of punch, he would need 12/2 = 6 containers of soda. Therefore, the total cost of the soda would be 6 x $3.00 = $18.00.
Now, we can calculate the total cost of the ingredients. The cost of the sorbet is $16.00 and the cost of the soda is $18.00, so the total cost of the ingredients is $16.00 + $18.00 = $34.00.
To make a $10 profit, Rafael needs to charge at least $34.00 + $10.00 = $44.00.
Since Rafael is making 12 cups of punch, he needs to charge $44.00 / 12 cups = $3.67 per cup of punch.
Therefore, the minimum amount Rafael should charge per cup of punch to make a $10 profit is $3.67.