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 12 cups of punch, which is equivalent to 3 quarts since there are 4 quarts in a gallon.
He needs 1 gallon of raspberry sorbet, which is equivalent to 4 quarts.
Therefore, he needs a total of 4 + 3 = 7 quarts of raspberry sorbet and lemon-lime soda.
Rafael pays $4.00 for a quart of sorbet and $3.00 for a 2-liter container of lemon-lime soda.
To find the total cost of the sorbet, divide the total quarts by the quarts per container: 7 quarts / 4 quarts = 1.75 containers of sorbet.
To find the total cost of the soda, divide the total quarts by the quarts per container: 7 quarts / 2 quarts = 3.5 containers of soda.
To find the total cost, multiply the number of containers of each item by their respective prices: 1.75 containers * $4/container + 3.5 containers * $3/container = $7.00 + $10.50 = $17.50.
To make a $10 profit, Rafael should charge $17.50 + $10 = $<<17.5+10=27.50>>27.50.
Since he wants to make a $10 profit and needs to sell 12 cups of punch, he should charge $27.50 / 12 cups = $<<27.5/12=2.29>>2.29 per cup of punch.
Rounded to the nearest hundredth, Rafael should charge $2.29 per cup of punch to make a $10 profit. Answer: \boxed{2.29}.
First, we need to find out the total cost of the ingredients Rafael needs for the punch.
1 gallon of raspberry sorbet is equal to 4 quarts.
So, Rafael needs (4 quarts) * ($4.00 per quart) = $<<4*4=16.00>>16.00 for the raspberry sorbet.
Rafael needs 2 liters of lemon-lime soda.
We know that he pays $3.00 for a 2-liter container of lemon-lime soda.
Next, we need to find the total cost of the ingredients.
Total cost of sorbet + Total cost of soda = $16.00 + $3.00 = $<<16+3=19.00>>19.00
Now, we can find the cost per cup of punch by dividing the total cost by the number of cups.
Total cost / Number of cups = $19.00 / 12 cups = $<<19/12=1.58>>1.58 per cup
To make a $10 profit, we need to add the profit to the cost per cup.
Cost per cup + Profit per cup = $1.58 + $10.00 = $<<1.58+10=11.58>>11.58 per cup
Therefore, Rafael should charge $11.58 per cup to make a $10 profit.
To find the minimum amount Rafael should charge per cup of punch to make a $10 profit, we need to consider the cost of the ingredients and the number of cups.
First, let's calculate the cost of the ingredients. Rafael needs a gallon of raspberry sorbet, which is equivalent to 4 quarts. Given that he pays $4.00 for a quart of sorbet, the total cost of sorbet is 4 * $4.00 = $16.00.
Next, Rafael needs 2 liters of lemon-lime soda. He pays $3.00 for a 2-liter container. So the cost of soda is $3.00.
Now, let's calculate the total cost of the ingredients. The total cost is $16.00 for sorbet + $3.00 for soda = $19.00.
Rafael wants to make a profit of $10. So, the cost of the ingredients plus the profit should equal $19.00 + $10.00 = $29.00.
Since Rafael wants to make 12 cups, the cost per cup should be $29.00 / 12 = $2.42.
Therefore, the minimum amount Rafael should charge per cup of punch to make a $10 profit is approximately $2.42.