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.
To make 12 cups of punch, Rafael needs 1 gallon of raspberry sorbet and 2 liters of lemon-lime soda. Since there are 4 quarts in a gallon, Rafael needs 4 * 1 = <<4*1=4>>4 quarts of sorbet.
So, Rafael needs a total of 4 quarts + 2 liters = <<4+2=6>>6 quarts + liters.
Since 1 quart is equal to 0.25 gallons, then 1 liter is equal to 0.25 liters and 2 liters is equal to 0.5 liters.
Therefore, Rafael needs a total of 6 * 0.25 = 1.50 gallons of lemon-lime soda and sorbet.
To make a profit of $10, Rafael should charge a total of $10 + $4 (cost of sorbet) + $3 (cost of soda) = $10 + $4 + $3 = $17.
To find out the total number of cups he can make with 1.50 gallons, we multiply 1.50 gallons by 16 cups per gallon (1 gallon is equal to 16 cups). This gives us 1.50 * 16 = 24 cups.
To find the minimum amount he should charge per cup of punch, we divide the total amount he should charge ($17) by the total number of cups he can make (24 cups). This gives us $17 / 24 cups = $0.71 per cup.
Therefore, the minimum amount Rafael should charge per cup of punch to make a $10 profit is $0.71, rounded to the nearest hundredth. Answer: $0.71.
wrong
I apologize for the mistake. Let's redo the calculations:
To make 12 cups of punch, Rafael needs 1 gallon of raspberry sorbet and 2 liters of lemon-lime soda. Since there are 4 quarts in a gallon, he needs 4 quarts of sorbet.
Rafael pays $4.00 for a quart of sorbet, so he pays 4 * 4 = $<<4*4=16.00>>16.00 for a gallon of sorbet.
He pays $3.00 for a 2-liter container of soda, which is equivalent to 2 / 2.11338 = 0.94635 gallons.
Therefore, Rafael pays a total of 16.00 + 3.00 = $<<16+3=19.00>>19.00 for the ingredients.
To make a $10.00 profit, he needs to earn 19.00 + 10.00 = $<<19+10=29.00>>29.00 in total.
Since he wants to make 12 cups of punch, he should charge 29.00 / 12 = $<<29/12=2.42>>2.42 per cup of punch.
Therefore, the minimum amount Rafael should charge per cup of punch to make a $10 profit is $2.42, rounded to the nearest hundredth. Answer: $2.42.
To determine the minimum amount Rafael should charge per cup of punch, we need to calculate the cost of the ingredients per cup, including the profit he wants to make.
First, let's calculate the cost of the lemon-lime soda per cup:
- Rafael pays $3.00 for a 2-liter container of soda.
- Since there are 2 liters in the container, that means there are 2 * 33.8 = 67.6 fluid ounces.
- Since 1 cup is equal to 8 fluid ounces, the cost of 1 cup of soda is 3.00 / (67.6 / 8) = $0.38.
Next, let's calculate the cost of the raspberry sorbet per cup:
- Rafael pays $4.00 for a quart of sorbet.
- Since there are 4 quarts in a gallon, that means there are 4 * 0.25 = 1 gallon of sorbet.
- Since there are 16 cups in a gallon, the cost of 1 cup of sorbet is 4.00 / 16 = $0.25.
Now, let's calculate the total cost of the ingredients per cup:
- Rafael needs 1 gallon of sorbet and 2 liters of soda to make 12 cups of punch.
- The total cost of the sorbet per cup is 0.25.
- The total cost of the soda per cup is 0.38.
- Adding these costs together, the total cost of the ingredients per cup is 0.25 + 0.38 = $0.63.
To calculate the minimum amount Rafael should charge per cup to make a $10 profit, we add the cost of the ingredients per cup to the desired profit per cup:
- The total cost of the ingredients per cup is $0.63.
- Rafael wants to make a $10 profit, so the desired profit per cup is 10 / 12 = $0.83.
Finally, we add the cost of the ingredients per cup to the desired profit per cup to find the minimum amount Rafael should charge:
- The minimum amount Rafael should charge per cup is 0.63 + 0.83 = $1.46 (rounded to the nearest hundredth).
Therefore, Rafael should charge at least $1.46 per cup of punch to make a $10 profit.