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)
First, we need to calculate how many quarts are in a gallon by dividing a gallon by 4: 1 gallon / 4 quarts/gallon = 0.25 gallons/quart.
Then we multiply this number by the number of quarts Rafael needs to find how many gallons of sorbet he needs: 0.25 gallons/quart * 1 quart = <<0.25*1=0.25>>0.25 gallons.
Then we multiply this number by the number of cups per gallon to find how many cups of sorbet he needs: 0.25 gallons * 12 cups/gallon = <<0.25*12=3>>3 cups.
Then we multiply the price of one quart of sorbet by the number of quarts Rafael needs to find how much the sorbet costs: $4/quart * 1 quart = $<<4*1=4>>4.
Then we multiply the number of liters in a 2-liter container by the number of containers Rafael needs to find how many liters of soda he needs: 2 liters/container * 1 container = <<2*1=2>>2 liters.
Then we multiply the number of liters by the number of cups per liter to find how many cups of soda Rafael needs: 2 liters * 4 cups/liter = <<2*4=8>>8 cups.
Then we multiply the price per liter of soda by the number of liters Rafael needs to find how much he spends on soda: $3/liter * 2 liters = $<<3*2=6>>6.
Then we add the cost of the sorbet and the soda to find Rafael's total costs: $6 + $4 = $<<6+4=10>>10.
Then we add Rafael's desired profit of $10 to find the total amount he wants to make: $10 + $10 = $<<10+10=20>>20.
Then we divide the total amount Rafael wants to make by the total number of cups to find the price per cup: $20 / 12 cups = $<<20/12=1.67>>1.67. Answer: \boxed{1.67}.
wrong
Apologies for the mistake. Let's correct it.
To make 12 cups of punch, Rafael needs 1 gallon of raspberry sorbet, which is 4 quarts. He also needs 2 liters of lemon-lime soda, which is approximately 2.11 quarts.
To calculate the cost of sorbet, Rafael needs to buy 4 quarts, so the total cost of sorbet is 4 quarts * $4/quart = $16.
Similarly, Rafael needs to buy 2.11 quarts of soda, which costs $3/liter. So, the total cost of soda is 2.11 quarts * $3/quart = $6.33.
Therefore, Rafael's total cost for making the punch is $16 + $6.33 = $22.33.
Now, Rafael wants to make a $10 profit. So he needs to charge a total of $22.33 + $10 = $32.33.
Since Rafael needs to make 12 cups of punch, he should charge $32.33 / 12 cups ≈ $2.69 per cup.
Thus, the minimum amount Rafael should charge per cup of punch to make a $10 profit is approximately $2.69.