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 12 cups of punch, Rafael needs to use 1 gallon of raspberry sorbet and 2 liters of lemon-lime soda.
There are 4 quarts in 1 gallon, so 1 gallon is equivalent to 4 quarts. A quart of sorbet costs $4.00, so 1 gallon of sorbet would cost $4.00 x 4 = $<<4*4=16.00>>16.00.
2 liters of soda costs $3.00, so 1 liter of soda would cost $3.00 / 2 = $<<3/2=1.50>>1.50.
Since Rafael needs 2 liters of soda, he would need to spend $1.50 x 2 = $<<1.50*2=3.00>>3.00 on soda.
In total, Rafael would spend $16.00 + $3.00 = $<<16+3=19.00>>19.00 on ingredients.
To make a $10 profit, Rafael needs to charge at least $19.00 + $10.00 = $<<19+10=29.00>>29.00.
Since he is making 12 cups of punch, he needs to charge at least $29.00 / 12 = $<<29/12=2.42>>2.42 per cup to make a $10 profit. Answer: \boxed{2.42}.
To calculate the minimum amount Rafael should charge per cup of punch, we need to determine the total cost of the ingredients and the desired profit.
First, let's calculate the cost of the ingredients:
- Rafael needs a gallon of raspberry sorbet, which equals 4 quarts. He pays $4.00 for each quart, so the cost of the sorbet is 4 quarts * $4.00/quart = $16.00.
- He also needs 2 liters of lemon-lime soda. He pays $3.00 for a 2-liter container, so the cost of the soda is $3.00.
Now, let's calculate the total cost:
- The total cost is the sum of the cost of the sorbet and the cost of the soda: $16.00 + $3.00 = $19.00.
Rafael wants to make a $10.00 profit. Therefore, the total amount he needs to make from selling the punch is $19.00 (the cost) + $10.00 (the desired profit) = $29.00.
Next, we need to determine how many cups are made from the given quantities. Since there are 12 cups, Rafael needs to charge a total of $29.00 / 12 cups ≈ $2.42 per cup.
Thus, the minimum amount Rafael should charge per cup of punch to make a $10 profit is approximately $2.42.
To make 1 gallon of punch, Rafael needs 4 quarts of sorbet.
So, to make 12 cups of punch, Rafael needs 4 quarts/12 cups = 1/3 quart of sorbet.
Since a quart of sorbet costs $4.00, 1/3 quart of sorbet would cost $4.00/3 = $1.33.
Rafael also needs 2 liters of lemon-lime soda, which costs $3.00.
Therefore, the total cost of ingredients for 12 cups of punch is $1.33 + $3.00 = $4.33.
To make a $10 profit, Rafael needs to charge at least $4.33 + $10.00 = $14.33.
Since he is selling 12 cups of punch, he should charge $14.33/12 = $1.19 per cup.
Therefore, the minimum amount he should charge per cup of punch to make a $10 profit is $1.19.
but what is the final answer
Sorry for the confusion. The final answer is that Rafael should charge a minimum of $1.19 per cup of punch in order to make a $10 profit.
wrong
Apologies for the incorrect response. Let me correct it.
To determine the minimum amount Rafael should charge per cup of punch, we need to divide the total cost by the number of cups.
The total cost of the ingredients is $19.00 and Rafael wants to make a $10.00 profit. So, the total amount he needs to make from selling the punch is $19.00 + $10.00 = $29.00.
Since there are 12 cups of punch, Rafael needs to charge at least $29.00 / 12 cups ≈ $2.42 per cup to make a $10 profit. Therefore, the correct answer is $2.42.