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.(1 point)
To find out how long it will take Karen to do her homework, we need to calculate the time it takes her to complete each task and then add the times together.
Karen can read 10 pages in 30 minutes, so she can read 1 page in 30/10 = <<30/10=3>>3 minutes.
Therefore, it will take her 3 minutes x 30 pages = <<3*30=90>>90 minutes to read all 30 pages.
Karen can complete 15 math problems in 30 minutes, so she can complete 1 math problem in 30/15 = <<30/15=2>>2 minutes.
Therefore, it will take her 2 minutes x 45 problems = <<2*45=90>>90 minutes to complete all 45 math problems.
In total, it will take Karen 90 minutes + 90 minutes = <<90+90=180>>180 minutes to do her homework. Answer: \boxed{180}.
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, which is equivalent to 4 quarts. He also needs 2 liters of lemon-lime soda.
The total cost of the sorbet is $4.00, and the total cost of the soda is $3.00.
To make a profit of $10 selling 12 cups of punch, Rafael needs to set the price per cup to cover his costs and make the desired profit.
First, we need to calculate the total cost of the punch:
Total cost = cost of sorbet + cost of soda = $4.00 + $3.00 = $7.00
Next, we need to determine the cost per cup:
Cost per cup = total cost / number of cups = $7.00 / 12 cups = $0.5833...
To make a $10 profit, Rafael needs to add this profit to the cost per cup:
Selling price per cup = cost per cup + profit per cup = $0.5833... + $10.00 / 12 cups = $0.9166...
Rounded to the nearest hundredth, the minimum amount Rafael should charge per cup of punch to make a $10 profit is $0.92. Answer: \boxed{0.92}.
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.(1 point)
To find out how much oil Randi will need for 8 gallons of gas, we can use the given ratio of 5 gallons of gas for every 2 gallons of oil.
Using a proportion, we can set up the following equation:
5 gallons of gas / 2 gallons of oil = 8 gallons of gas / x (gallons of oil)
Cross-multiplying, we get:
5x = 8 * 2
5x = 16
Dividing both sides by 5, we find:
x = 16 / 5
x = 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.(1 point)
To determine which paver is the best buy, we need to compare the cost per paver for each type.
Given the following information:
Paver 1: $1.49 each
Paver 2: $2.50 each
Paver 3: $0.75 each
Paver 1 requires twice as many pavers as Paver 2 and half as many pavers as Paver 3. Therefore, the ratio of the number of Paver 1 to Paver 2 is 2:1, and the ratio of the number of Paver 1 to Paver 3 is 1:0.5 or 2:1.
To compare the cost per paver, we can multiply the cost by the ratio:
For Paver 1: $1.49 * 2 = $2.98
For Paver 2: $2.50 * 1 = $2.50
For Paver 3: $0.75 * 1 = $0.75
From the calculations, we can see that Paver 3 has the lowest cost per paver at $0.75.
Therefore, Paver 3 is the best buy. Answer: \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?(1 point)
Responses
50 students
50 students
124 students
124 students
250 students
250 students
200 students
To solve this problem, we need to use the proportional relationship between the number of seats in choir and band.
Given that there are four times as many seats in choir as there are in band, we can set up the following equation:
Number of Choir seats = 4 * Number of Band seats.
Let's represent the number of band seats as 'x'. Therefore, the number of choir seats will be 4x.
The problem tells us that there is a total of 250 students. Since each student can only choose one elective, the total number of seats in choir and band must add up to 250.
So, we can set up the equation:
Number of Choir seats + Number of Band seats = Total number of students
4x + x = 250
Combining like terms, we get:
5x = 250
Dividing both sides by 5, we find:
x = 50
Therefore, there are 50 seats available in the band.
So, the answer is: 50 students can choose band if there is a total of 250 students. Answer: \boxed{50}.
Carla needs to complete her science homework. She has 20 pages to read and 14 questions to answer. If it takes Carla 10 minutes to read 4 pages, how many minutes will it take her to read the full assignment?(1 point)
Responses
50 minutes
50 minutes
9 minutes
9 minutes
85 minutes
85 minutes
35 minutes