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?
To find out the minimum amount Rafael should charge per cup of punch to make a $10 profit, we need to calculate his total cost and then add the desired profit.
First, let's find out the total cost of the ingredients:
- Rafael needs 2 liters of lemon-lime soda, which costs $3.00 per 2-liter container. This means the cost of the soda is $3.00.
- He needs a gallon of raspberry sorbet, which is equivalent to 4 quarts. Rafael pays $4.00 for a quart of sorbet, so the total cost of the sorbet is $4.00 x 4 = $16.00.
Now let's calculate the total cost:
Total cost = Cost of soda + Cost of sorbet
Total cost = $3.00 + $16.00
Total cost = $19.00
To make a $10 profit, Rafael needs to add this amount to his total cost:
Total cost + Desired profit = Minimum amount to charge
$19.00 + $10.00 = $29.00
Since Rafael wants to make a profit of $10 and he is making 12 cups, the minimum amount he should charge per cup is:
Minimum amount to charge per cup = Total amount to charge / Number of cups
$29.00 / 12 cups = $2.42 (rounded to the nearest cent)
Therefore, Rafael should charge at least $2.42 per cup of punch to make a $10 profit.
First find how many quarts are in 1 gallon: 1 gallon * 4 quarts/gallon = <<1*4=4>>4 quarts
Then multiply that number by the price per quart to find how much the sorbet cost: $4.00/quart * 4 quarts = $<<4*4=16.00>>16.00
Then multiply the number of liters Rafael buys by the price per liter to find how much the soda cost: $3.00/liter * 2 liters = $6.00
Now divide Rafael's total costs by the number of cups he makes to find his cost per cup: $16.00 + $6.00 = $<<16+6=22.00>>22.00
Finally, add Rafael's desired profit to find the total cost per cup: $10.00 + $22.00 = $<<10+22=32.00>>32.00. Answer: \boxed{32}.
To find 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.
The total cost of the lemon-lime soda can be found by dividing the cost per 2-liter container by the number of cups in a 2-liter container. Since there are 12 cups in a gallon, and a gallon is equivalent to 2 liters, there would be approximately (2/12) * 2 = 1/6 liters of soda per cup. Therefore, the cost of soda per cup is (3.00 / 2) / (1/6) = 9 / 2 dollars.
Next, we need to calculate the total cost of the sorbet. Since Rafael needs a gallon of sorbet and there are 4 quarts in a gallon, each cup requires 4/12 = 1/3 quart of sorbet. Therefore, the cost of sorbet per cup is 4.00 / (1/3) = 12.00 dollars.
Now, we can find the total cost per cup by adding the costs of soda and sorbet per cup: 9/2 +12 = 33/2 = 16.50 dollars.
To make a $10 profit per cup, Rafael needs to charge at least the total cost per cup plus the desired profit: 16.50 + 10 = 26.50 dollars.
Therefore, Rafael should charge at least $26.50 per cup of punch to make a $10 profit.