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 make the punch, Rafael needs a gallon of raspberry sorbet and 2 liters of lemon-lime soda. Since there are 4 quarts in a gallon, he needs to buy 4 * $4 = $<<4*4=16>>16 worth of sorbet.
He also needs to buy enough soda to fill 12 cups. Since there are 4 cups in a liter, he will need 12 / 4 = 3 liters of soda.
At $3 per 2-liter container, he will need to buy 3 / 2 * $3 = $<<3/2*3=4.5>>4.5 worth of soda.
In total, Rafael's cost for the ingredients is $16 + $4.5 = $<<16+4.5=20.5>>20.5
To make a $10 profit, he needs to charge $20.5 + $10 = $<<20.5+10=30.5>>30.5
Since Rafael wants to sell 12 cups, he needs to charge $30.5 / 12 = $<<30.5/12=2.54>>2.54 per cup. Answer: \boxed{2.54}.
To find out 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 used to make 12 cups of punch and then add the desired profit of $10.
First, we need to determine how much sorbet is needed for 12 cups of punch. Since there are 4 quarts in a gallon, and Rafael needs a gallon of sorbet for 12 cups, he will need 4 quarts of sorbet for 12 cups. So, he will need to purchase 4 quarts of sorbet at a cost of $4.00 per quart, for a total cost of 4 * $4.00 = $16.00.
Next, we need to determine how much lemon-lime soda is needed for 12 cups of punch. Since Rafael needs 2 liters of soda for 12 cups, he will need to purchase 2 liters of soda at a cost of $3.00 per 2-liter container.
To calculate the total cost of ingredients, we add the cost of sorbet and soda: $16.00 + $3.00 = $19.00.
Now, we add the desired profit of $10 to the total cost of ingredients: $19.00 + $10.00 = $29.00.
Lastly, we divide the total cost by the number of cups (12) to get the minimum amount Rafael should charge per cup of punch: $29.00 / 12 = $2.42.
Therefore, Rafael should charge a minimum of $2.42 per cup of punch to make a $10 profit.
Step 1: Convert gallons to cups
- Since there are 4 quarts in a gallon and 4 cups in a quart, 1 gallon is equal to 4 x 4 = 16 cups.
Step 2: Calculate the total cost of the ingredients
- Rafael needs 1 gallon of raspberry sorbet, which is equal to 16 cups. Since he pays $4 for a quart of sorbet, the total cost of the sorbet is 4 x 4 = $16.
- Rafael needs 2 liters of lemon-lime soda, which is equal to 2 x 33.81 = 67.62 fluid ounces. Since he pays $3 for a 2-liter container of soda, the cost of the soda is $3.
Step 3: Calculate the total cost of making 12 cups of punch
- The cost of the sorbet per cup is $16 / 16 = $1.
- The cost of the soda per cup is $3 / 67.62 = $0.044.
- The total cost of making 12 cups of punch is (12 x $1) + (12 x $0.044) = $12 + $0.528 = $12.528.
Step 4: Calculate the minimum amount he should charge per cup to make a $10 profit
- The total cost of making 12 cups of punch is $12.528.
- Rafael wants to make a $10 profit, so the minimum amount he should charge per cup is ($12.528 + $10) / 12 = $22.528 / 12 = $1.877 rounded to the nearest hundredth.
Therefore, Rafael should charge at least $1.88 per cup of punch to make a $10 profit.