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!!!
Rafael needs 12 cups of punch.
To make the punch, he needs a gallon of raspberry sorbet, which is 4 quarts. So, he needs 4 quarts of sorbet divided by 12 cups, which is 1/3 of a quart of sorbet per cup.
Rafael needs 2 liters of lemon-lime soda, which is approximately 2.11 quarts. So, he needs 2.11 quarts of soda divided by 12 cups, which is approximately 0.176 of a quart of soda per cup.
To calculate the cost, Rafael paid $4.00 for the sorbet and $3.00 for the soda, which is a total of $4.00 + $3.00 = $7.00.
To make a profit of $10.00, Rafael should charge $7.00 + $10.00 = $17.00 for the punch.
Therefore, the minimum amount he should charge per cup of punch is $17.00 / 12 cups = $1.42 per cup, rounded to the nearest hundredth. Answer: \boxed{1.42}.
wrong :[
Apologies for the mistake in the previous response. Let's recalculate the minimum amount Rafael should charge per cup of punch to make a $10 profit.
Rafael needs 12 cups of punch, so he needs approximately 0.0833 gallons of raspberry sorbet since there are 4 quarts in a gallon. Therefore, he needs approximately 0.0833 * $4.00 = $0.3332 worth of sorbet per cup of punch.
Rafael also needs 2 liters of lemon-lime soda, which is approximately 0.5283 gallons. Therefore, he needs approximately 0.5283 * $3.00 = $1.5849 worth of soda per cup of punch.
The total cost of ingredients per cup of punch is approximately $0.3332 + $1.5849 = $1.9181.
To make a $10 profit, Rafael should charge $1.9181 + $10.00 = $11.9181 per cup of punch.
Therefore, the minimum amount he should charge per cup of punch to make a $10 profit is $11.92, rounded to the nearest hundredth. Answer: $11.92.
Randi needs to mow her lawn. The mixture requires 5 gallons of gas for every 2 gallons of oil. How much oil will she need for 8 gallons of gas? Your answer should be in tenths.
Based on the given mixture ratio, for every 5 gallons of gas, Randi needs 2 gallons of oil.
To find the amount of oil needed for 8 gallons of gas, we can set up a proportion:
5 gallons of gas / 2 gallons of oil = 8 gallons of gas / x gallons of oil
Cross-multiplying, we get:
5x = 16
Dividing both sides by 5, we find:
x = 16/5 = 3.2
Therefore, Randi will need 3.2 gallons of oil for 8 gallons of gas. Answer: \boxed{3.2}.
Laila is laying a path down for a new driveway. The store has three types of paver stones that will work for her space. She needs to know which paver is the best price. Paver 1 costs $1.49 each, and she will need twice as many as paver 2 and half as many as paver 3. Paver 2 costs $2.50 each. Paver 3 costs $0.75. Which paver will be the best buy? Your answer should be a number.
Let's calculate the total cost for each type of paver stone:
Paver 1:
Since Laila needs twice as many paver 1 as paver 2, let's assume she needs x paver 2 stones. Therefore, she needs 2x paver 1 stones.
The cost of each paver 1 stone is $1.49.
So, the total cost for paver 1 will be 2x * $1.49 = $2.98x.
Paver 2:
The cost of each paver 2 stone is $2.50.
Laila needs x paver 2 stones.
So, the total cost for paver 2 will be x * $2.50 = $2.50x.
Paver 3:
Laila needs half as many paver 3 stones as paver 1.
So, she needs (1/2)*(2x) = x paver 3 stones.
The cost of each paver 3 stone is $0.75.
Therefore, the total cost for paver 3 will be x * $0.75 = $0.75x.
Now, let's compare the total costs for each type of paver:
Paver 1: $2.98x
Paver 2: $2.50x
Paver 3: $0.75x
Since we are looking for the best price, we want the lowest total cost.
Comparing the prices, we can see that Paver 3 has the lowest total cost.
Therefore, Paver 3 will be the best buy. The answer is \boxed{0.75}.
Use proportional relationships to solve this mixture problem. The incoming 6th-grade class has a choice between band or choir as an elective. There are four times as many seats in choir as there are in band. How many students can choose band if there is a total of 250 students?
Let's denote the number of seats in band as x.
According to the problem, there are four times as many seats in choir as there are in band. Therefore, the number of seats in choir would be 4x.
Since the total number of students is 250 and all students must choose either band or choir, we can set up the following equation:
x + 4x = 250
Combining like terms, we get:
5x = 250
Dividing both sides of the equation by 5, we find:
x = 50
Therefore, there are 50 seats in the band, and thus the number of students that can choose band is 50.
Answer: 50 students.