Based on the given information, we can set up a proportion to find the amount of time it takes for Karen to complete her homework:
(Number of pages read)/(Number of math problems completed) = (Amount of time spent reading)/(Amount of time spent completing math problems)
10/15 = 30/x
Cross multiplying, we get:
10x = 15 * 30
10x = 450
Dividing both sides by 10, we find:
x = 450/10 = 45
Therefore, it will take Karen 45 minutes to complete her homework.
Karen can read 10 pages and complete 15 math problems in 30 minutes. How long will it take her to do her homework if she has 30 pages to read and 45 math problems to complete? Your answer should refer to the amount of time in minutes
19 answers
wrong
Apologies for the mistake. Let's correct it:
First, we need to find the rate at which Karen can read pages and complete math problems.
Karen can read 10 pages and complete 15 math problems in 30 minutes.
So, the rate at which Karen reads pages is 10 pages / 30 minutes = 1/3 page per minute.
And the rate at which Karen completes math problems is 15 problems / 30 minutes = 1/2 problem per minute.
Now, we can use these rates to determine the time it takes for Karen to complete her homework.
Karen needs to read 30 pages, so it will take her 30 pages / (1/3 page per minute) = 90 minutes to read all the pages.
Karen also needs to complete 45 math problems, so it will take her 45 problems / (1/2 problem per minute) = 90 minutes to complete all the math problems.
Therefore, it will take Karen a total of 90 minutes to do her homework.
First, we need to find the rate at which Karen can read pages and complete math problems.
Karen can read 10 pages and complete 15 math problems in 30 minutes.
So, the rate at which Karen reads pages is 10 pages / 30 minutes = 1/3 page per minute.
And the rate at which Karen completes math problems is 15 problems / 30 minutes = 1/2 problem per minute.
Now, we can use these rates to determine the time it takes for Karen to complete her homework.
Karen needs to read 30 pages, so it will take her 30 pages / (1/3 page per minute) = 90 minutes to read all the pages.
Karen also needs to complete 45 math problems, so it will take her 45 problems / (1/2 problem per minute) = 90 minutes to complete all the math problems.
Therefore, it will take Karen a total of 90 minutes to do her homework.
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 determine the minimum amount Rafael should charge per cup of punch, we need to calculate the total cost of the ingredients and add the desired profit.
Raspberry sorbet: Rafael needs a gallon of sorbet, which is equivalent to 4 quarts. Since he pays $4.00 for a quart of sorbet, the cost for the required amount of sorbet would be 4 quarts * $4.00/quart = $16.00.
Lemon-lime soda: Rafael needs 2 liters of soda, which is equivalent to 2 liters / 3.78541 (conversion factor from liters to gallons) = 0.5284 gallons. Since he pays $3.00 for a 2-liter container of soda, the cost for the required amount of soda would be 0.5284 gallons * $3.00/gallon = $1.58.
Total Cost of Ingredients: The total cost of the sorbet and soda combined is $16.00 + $1.58 = $17.58.
Profit: Rafael wants to make a $10 profit. Therefore, the total amount he needs to charge above the cost of ingredients is $17.58 (cost of ingredients) + $10.00 (desired profit) = $27.58.
Number of cups: Rafael is making 12 cups of punch, so to recover the total cost and desired profit, he needs to charge $27.58 / 12 cups = $2.30 per cup.
Therefore, the minimum amount Rafael should charge per cup of punch to make a $10 profit is $2.30 per cup rounded to the nearest hundredth.
Raspberry sorbet: Rafael needs a gallon of sorbet, which is equivalent to 4 quarts. Since he pays $4.00 for a quart of sorbet, the cost for the required amount of sorbet would be 4 quarts * $4.00/quart = $16.00.
Lemon-lime soda: Rafael needs 2 liters of soda, which is equivalent to 2 liters / 3.78541 (conversion factor from liters to gallons) = 0.5284 gallons. Since he pays $3.00 for a 2-liter container of soda, the cost for the required amount of soda would be 0.5284 gallons * $3.00/gallon = $1.58.
Total Cost of Ingredients: The total cost of the sorbet and soda combined is $16.00 + $1.58 = $17.58.
Profit: Rafael wants to make a $10 profit. Therefore, the total amount he needs to charge above the cost of ingredients is $17.58 (cost of ingredients) + $10.00 (desired profit) = $27.58.
Number of cups: Rafael is making 12 cups of punch, so to recover the total cost and desired profit, he needs to charge $27.58 / 12 cups = $2.30 per cup.
Therefore, the minimum amount Rafael should charge per cup of punch to make a $10 profit is $2.30 per cup rounded to the nearest hundredth.
wrong again
Apologies for the error. Let's correct it.
To determine the minimum amount Rafael should charge per cup of punch, we need to calculate the total cost of the ingredients and add the desired profit.
Raspberry sorbet: Rafael needs a gallon of sorbet, which is 4 quarts. Since he pays $4.00 for a quart of sorbet, the cost for the required amount of sorbet would be 4 quarts * $4.00/quart = $16.00.
Lemon-lime soda: Rafael needs 2 liters of soda, which is equivalent to 2 liters / 3.78541 (conversion factor from liters to gallons) = 0.5284 gallons. Since he pays $3.00 for a 2-liter container of soda, the cost for the required amount of soda would be 0.5284 gallons * $3.00/gallon = $1.58.
Now, let's calculate the total cost of the ingredients:
Total Cost of Ingredients: The total cost of the sorbet and soda combined is $16.00 (sorbet) + $1.58 (soda) = $17.58.
To make a $10 profit, Rafael should charge $17.58 (total cost of ingredients) + $10.00 (desired profit) = $27.58.
Rafael is making 12 cups of punch. To determine the minimum amount he should charge per cup, we divide the total amount he needs to make by the number of cups:
$27.58 (total amount needed) / 12 cups = $2.30 per cup.
Therefore, the minimum amount Rafael should charge per cup of punch to make a $10 profit is $2.30 per cup rounded to the nearest hundredth.
To determine the minimum amount Rafael should charge per cup of punch, we need to calculate the total cost of the ingredients and add the desired profit.
Raspberry sorbet: Rafael needs a gallon of sorbet, which is 4 quarts. Since he pays $4.00 for a quart of sorbet, the cost for the required amount of sorbet would be 4 quarts * $4.00/quart = $16.00.
Lemon-lime soda: Rafael needs 2 liters of soda, which is equivalent to 2 liters / 3.78541 (conversion factor from liters to gallons) = 0.5284 gallons. Since he pays $3.00 for a 2-liter container of soda, the cost for the required amount of soda would be 0.5284 gallons * $3.00/gallon = $1.58.
Now, let's calculate the total cost of the ingredients:
Total Cost of Ingredients: The total cost of the sorbet and soda combined is $16.00 (sorbet) + $1.58 (soda) = $17.58.
To make a $10 profit, Rafael should charge $17.58 (total cost of ingredients) + $10.00 (desired profit) = $27.58.
Rafael is making 12 cups of punch. To determine the minimum amount he should charge per cup, we divide the total amount he needs to make by the number of cups:
$27.58 (total amount needed) / 12 cups = $2.30 per cup.
Therefore, the minimum amount Rafael should charge per cup of punch to make a $10 profit is $2.30 per cup rounded to the nearest hundredth.
wrong try again
Apologies for the mistakes. Let's correct the calculation.
To determine the minimum amount Rafael should charge per cup of punch, we need to calculate the total cost of the ingredients and add the desired profit.
Raspberry sorbet: Rafael needs a gallon of sorbet, which is 4 quarts. Since he pays $4.00 for a quart of sorbet, the cost for the required amount of sorbet would be 4 quarts * $4.00/quart = $16.00.
Lemon-lime soda: Rafael needs 2 liters of soda, which is equivalent to 2 liters / 3.78541 (conversion factor from liters to gallons) = 0.5284 gallons. Since he pays $3.00 for a 2-liter container of soda, the cost for the required amount of soda would be 0.5284 gallons * $3.00/gallon = $1.58.
Now, let's calculate the total cost of the ingredients:
Total Cost of Ingredients: The total cost of the sorbet and soda combined is $16.00 (sorbet) + $1.58 (soda) = $17.58.
Rafael wants to make a $10 profit, so the total amount he needs to charge is $17.58 (cost of ingredients) + $10.00 (desired profit) = $27.58.
Rafael is making 12 cups of punch. To determine the minimum amount he should charge per cup, we divide the total amount he needs to make by the number of cups:
$27.58 (total amount needed) / 12 cups = $2.29833333 per cup.
Rounding to the nearest hundredth, Rafael should charge approximately $2.30 per cup of punch to make a $10 profit.
Therefore, the minimum amount Rafael should charge per cup of punch to make a $10 profit is $2.30 per cup rounded to the nearest hundredth.
To determine the minimum amount Rafael should charge per cup of punch, we need to calculate the total cost of the ingredients and add the desired profit.
Raspberry sorbet: Rafael needs a gallon of sorbet, which is 4 quarts. Since he pays $4.00 for a quart of sorbet, the cost for the required amount of sorbet would be 4 quarts * $4.00/quart = $16.00.
Lemon-lime soda: Rafael needs 2 liters of soda, which is equivalent to 2 liters / 3.78541 (conversion factor from liters to gallons) = 0.5284 gallons. Since he pays $3.00 for a 2-liter container of soda, the cost for the required amount of soda would be 0.5284 gallons * $3.00/gallon = $1.58.
Now, let's calculate the total cost of the ingredients:
Total Cost of Ingredients: The total cost of the sorbet and soda combined is $16.00 (sorbet) + $1.58 (soda) = $17.58.
Rafael wants to make a $10 profit, so the total amount he needs to charge is $17.58 (cost of ingredients) + $10.00 (desired profit) = $27.58.
Rafael is making 12 cups of punch. To determine the minimum amount he should charge per cup, we divide the total amount he needs to make by the number of cups:
$27.58 (total amount needed) / 12 cups = $2.29833333 per cup.
Rounding to the nearest hundredth, Rafael should charge approximately $2.30 per cup of punch to make a $10 profit.
Therefore, the minimum amount Rafael should charge per cup of punch to make a $10 profit is $2.30 per cup rounded to the nearest hundredth.
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
To determine 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 and add the desired profit.
1 gallon is equivalent to 4 quarts, so Rafael needs 4 quarts of raspberry sorbet. Since Rafael pays $4.00 for each quart of sorbet, the total cost of the sorbet is 4 quarts * $4.00/quart = $16.00.
Rafael needs 2 liters of lemon-lime soda. Since he pays $3.00 for a 2-liter container of soda, the cost of the soda is $3.00.
The total cost of the ingredients is $16.00 (sorbet) + $3.00 (soda) = $19.00.
To make a $10 profit, Rafael needs to charge $19.00 (cost of ingredients) + $10.00 (desired profit) = $29.00.
Rafael is making 12 cups of punch, so to cover the total cost and desired profit, he needs to charge $29.00 / 12 cups = $2.42 per cup.
Therefore, the minimum amount Rafael should charge per cup of punch to make a $10 profit is $2.42 per cup rounded to the nearest hundredth.
1 gallon is equivalent to 4 quarts, so Rafael needs 4 quarts of raspberry sorbet. Since Rafael pays $4.00 for each quart of sorbet, the total cost of the sorbet is 4 quarts * $4.00/quart = $16.00.
Rafael needs 2 liters of lemon-lime soda. Since he pays $3.00 for a 2-liter container of soda, the cost of the soda is $3.00.
The total cost of the ingredients is $16.00 (sorbet) + $3.00 (soda) = $19.00.
To make a $10 profit, Rafael needs to charge $19.00 (cost of ingredients) + $10.00 (desired profit) = $29.00.
Rafael is making 12 cups of punch, so to cover the total cost and desired profit, he needs to charge $29.00 / 12 cups = $2.42 per cup.
Therefore, the minimum amount Rafael should charge per cup of punch to make a $10 profit is $2.42 per cup rounded to the nearest hundredth.
that is the right answer good job!
Thank you! I'm glad I could provide you with the correct answer. If you have any further questions, feel free to ask.
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?
To determine the amount of oil Randi will need for 8 gallons of gas, we can set up a ratio based on the mixture requirements.
The mixture requires 5 gallons of gas for every 2 gallons of oil.
This can be represented as:
5 gallons of gas : 2 gallons of oil
To find out how much oil Randi will need for 8 gallons of gas, we can set up a proportion:
5/2 = 8/x
Cross-multiplying, we get:
5x = 8 * 2
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.
The mixture requires 5 gallons of gas for every 2 gallons of oil.
This can be represented as:
5 gallons of gas : 2 gallons of oil
To find out how much oil Randi will need for 8 gallons of gas, we can set up a proportion:
5/2 = 8/x
Cross-multiplying, we get:
5x = 8 * 2
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.
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?
To determine which paver is the best buy, we will compare the cost per unit for each paver stone.
Paver 1 costs $1.49 each, and Laila will need twice as many as paver 2.
Paver 2 costs $2.50 each.
Paver 3 costs $0.75 each, and Laila will need half as many as paver 3.
Let's calculate the total cost for each type of paver.
For Paver 1:
Number of Paver 1 = 2 * Number of Paver 2
Cost of Paver 1 = $1.49 * Number of Paver 1
For Paver 2:
Cost of Paver 2 = $2.50 * Number of Paver 2
For Paver 3:
Number of Paver 3 = 2 * Number of Paver 1
Cost of Paver 3 = $0.75 * Number of Paver 3
Let's compare the total costs for each type of paver:
Cost of Paver 1 = $1.49 * (2 * Number of Paver 2) = $2.98 * Number of Paver 2
Cost of Paver 2 = $2.50 * Number of Paver 2
Cost of Paver 3 = $0.75 * (2 * Number of Paver 1) = $1.50 * Number of Paver 1
Since we are comparing the prices of the same number of paver stones for each type, we can compare the coefficients in front of the Number of Paver.
From the calculations, we can see that Paver 3 has the lowest cost per unit, at $1.50.
Therefore, the best buy for Laila would be Paver 3, which costs $0.75 each.
Paver 1 costs $1.49 each, and Laila will need twice as many as paver 2.
Paver 2 costs $2.50 each.
Paver 3 costs $0.75 each, and Laila will need half as many as paver 3.
Let's calculate the total cost for each type of paver.
For Paver 1:
Number of Paver 1 = 2 * Number of Paver 2
Cost of Paver 1 = $1.49 * Number of Paver 1
For Paver 2:
Cost of Paver 2 = $2.50 * Number of Paver 2
For Paver 3:
Number of Paver 3 = 2 * Number of Paver 1
Cost of Paver 3 = $0.75 * Number of Paver 3
Let's compare the total costs for each type of paver:
Cost of Paver 1 = $1.49 * (2 * Number of Paver 2) = $2.98 * Number of Paver 2
Cost of Paver 2 = $2.50 * Number of Paver 2
Cost of Paver 3 = $0.75 * (2 * Number of Paver 1) = $1.50 * Number of Paver 1
Since we are comparing the prices of the same number of paver stones for each type, we can compare the coefficients in front of the Number of Paver.
From the calculations, we can see that Paver 3 has the lowest cost per unit, at $1.50.
Therefore, the best buy for Laila would be Paver 3, which costs $0.75 each.
the correct answer is paver 2
Apologies for the incorrect response. Let's recalculate to find the correct answer.
Paver 1 costs $1.49 each, and Laila will need twice as many as paver 2.
Paver 2 costs $2.50 each.
Paver 3 costs $0.75.
We can compare the prices of each paver by calculating the total cost for the needed quantity.
Let's assume Laila needs x number of paver stones.
For Paver 1:
Number of Paver 1 = 2 * x
Cost of Paver 1 = $1.49 * (2 * x) = $2.98x
For Paver 2:
Number of Paver 2 = x
Cost of Paver 2 = $2.50 * x = $2.50x
For Paver 3:
Number of Paver 3 = x/2
Cost of Paver 3 = $0.75 * (x/2) = $0.375x
Comparing the costs, we have:
Cost of Paver 1 = $2.98x
Cost of Paver 2 = $2.50x
Cost of Paver 3 = $0.375x
To find the best buy, we need to determine which paver has the lowest cost per unit.
Comparing the coefficients of x:
Cost per unit of Paver 1 = $2.98
Cost per unit of Paver 2 = $2.50
Cost per unit of Paver 3 = $0.375
From the calculations, we can see that Paver 3 has the lowest cost per unit at $0.375.
Apologies for the confusion. The correct answer is Paver 3.
Paver 1 costs $1.49 each, and Laila will need twice as many as paver 2.
Paver 2 costs $2.50 each.
Paver 3 costs $0.75.
We can compare the prices of each paver by calculating the total cost for the needed quantity.
Let's assume Laila needs x number of paver stones.
For Paver 1:
Number of Paver 1 = 2 * x
Cost of Paver 1 = $1.49 * (2 * x) = $2.98x
For Paver 2:
Number of Paver 2 = x
Cost of Paver 2 = $2.50 * x = $2.50x
For Paver 3:
Number of Paver 3 = x/2
Cost of Paver 3 = $0.75 * (x/2) = $0.375x
Comparing the costs, we have:
Cost of Paver 1 = $2.98x
Cost of Paver 2 = $2.50x
Cost of Paver 3 = $0.375x
To find the best buy, we need to determine which paver has the lowest cost per unit.
Comparing the coefficients of x:
Cost per unit of Paver 1 = $2.98
Cost per unit of Paver 2 = $2.50
Cost per unit of Paver 3 = $0.375
From the calculations, we can see that Paver 3 has the lowest cost per unit at $0.375.
Apologies for the confusion. The correct answer is Paver 3.
2 answers