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)
To find the minimum amount Rafael 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 cost of the lemon-lime soda. Rafael pays $3.00 for a 2-liter container, so the cost of 1 liter of soda is $3.00 / 2 = $1.50. Since there are 2 liters of soda required, the total cost of soda is 2 * $1.50 = $3.00.
Next, let's calculate the cost of the raspberry sorbet. Rafael pays $4.00 for a quart of sorbet, and there are 4 quarts in a gallon. So the cost of 1 quart of sorbet is $4.00 / 4 = $1.00. Since a gallon is required, the total cost of sorbet is 1 * $1.00 = $1.00.
Now let's calculate the total cost of the ingredients. The total cost is $3.00 (soda) + $1.00 (sorbet) = $4.00.
To determine the minimum amount Rafael should charge per cup of punch to make a $10 profit, we need to divide the total cost of the ingredients and the profit by the number of cups.
Since there are 12 cups, the minimum amount Rafael should charge per cup to cover his costs and make a $10 profit is ($4.00 + $10.00) / 12 = $14.00 / 12 = $1.17 (rounded to the nearest hundredth).
So, Rafael should charge approximately $1.17 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 need to calculate the cost of the ingredients and then add the desired profit.
1. Rafael needs a gallon of raspberry sorbet, which is equal to 4 quarts. He pays $4.00 per quart, so the total cost of the sorbet is 4 quarts * $4.00/quart = $<<4*4=16.00>>16.00.
2. Rafael needs 2 liters of lemon-lime soda, for which he pays $3.00 per 2-liter container. Since a gallon is equal to 3.785 liters, he needs 3.785 liters / 2 liters/container = 1.893 containers of soda. Rounded up to the nearest whole number, this means he needs 2 containers.
The total cost for the lemon-lime soda is 2 containers * $3.00/container = $<<2*3=6.00>>6.00.
3. The total cost of the ingredients is $16.00 + $6.00 = $<<16+6=22.00>>22.00.
4. Rafael wants to make a $10.00 profit, so he needs to charge at least $22.00 + $10.00 = $32.00 in total.
5. Rafael needs to make 12 cups, so the minimum amount he should charge per cup is $32.00 / 12 cups = $<<32/12=2.67>>2.67.
Therefore, Rafael should charge a minimum of $2.67 per cup of punch to make a $10 profit.
To make 12 cups of punch, Rafael needs a gallon of raspberry sorbet, which is 4 quarts. So, he needs 4 quarts * $4.00/quart = $<<4*4=16.00>>16.00 worth of sorbet.
He also needs 2 liters of lemon-lime soda, which costs $3.00 per 2-liter container.
Since there are 12 cups in total, Rafael needs to divide the cost of the ingredients by 12 to find the cost per cup.
The total cost of the ingredients is $16.00 + $3.00 = $19.00.
Therefore, Rafael should charge $19.00 / 12 cups = $<<19/12=1.58>>1.58 per cup.
To make a $10 profit, Rafael needs to charge $1.58 + $10.00 = $<<1.58+10=11.58>>11.58 per cup.
Thus, the minimum amount he should charge per cup of punch to make a $10 profit is $11.58. Answer: \boxed{11.58}.