The ratio of girls to boys in the school is 3 to 1. If there is a total of 400 students, how many are boys? The answer must be a whole number.(1 point)
The ratio of girls to boys is 3 to 1. This means that out of every 3 students, 3 are girls and 1 is a boy.
To find the number of boys, we need to find 1 part out of every 4 parts (3 parts for girls and 1 part for boys).
The total number of parts is 4 (3 parts for girls and 1 part for boys).
To find the number of boys, we need to divide the total number of students by the total number of parts and then multiply that by the number of parts that represent boys.
Number of boys = (Total number of students / Total number of parts) * Number of parts for boys
Number of boys = (400 / 4) * 1
Number of boys = (100) * 1
Number of boys = 100
Therefore, there are 100 boys in the school.
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)
We can set up a ratio based on the work Karen can do in 30 minutes:
10 pages / 15 math problems = 30 minutes
Now we can use this ratio to find out how long it will take Karen to do her homework:
30 pages / 45 math problems = x minutes
To solve for x, we can use cross multiplication:
30 * 15 = 10 * x
450 = 10x
Now we can solve for x by dividing both sides of the equation by 10:
450 / 10 = x
45 = x
Therefore, it will take Karen 45 minutes to complete her homework.
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I apologize for the mistake. Let's correct it.
Based on the given information, we know that Karen can complete 10 pages and 15 math problems in 30 minutes. To find out how long it will take her to do her homework, we need to calculate the amount of time it takes for her to complete one page and one math problem.
In 30 minutes, Karen can do 10 pages and 15 math problems. Therefore, it takes her 30/10 = 3 minutes to complete one page, and 30/15 = 2 minutes to complete one math problem.
Now, let's find out how long it will take her to complete her homework, which includes 30 pages and 45 math problems.
To complete 30 pages at a rate of 3 minutes per page, it will take her 30 * 3 = 90 minutes.
To complete 45 math problems at a rate of 2 minutes per problem, it will take her 45 * 2 = 90 minutes.
Therefore, it will take Karen a total of 90 + 90 = 180 minutes to complete 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.(1 point)
To find the minimum amount Rafael should charge per cup of punch, we need to calculate his total cost and add the desired profit.
First, let's calculate the cost of the ingredients:
- Rafael needs a gallon of raspberry sorbet, which is equivalent to 4 quarts. Since he pays $4.00 for a quart, the cost of the sorbet is 4 * $4.00 = $16.00.
- Rafael needs 2 liters of lemon-lime soda. He pays $3.00 for 2 liters, which is the same as $3.00 for 2 * 33.8 ounces = $3.00 for 67.6 ounces.
Next, let's calculate the cost per cup of each ingredient:
- Rafael needs 12 cups of punch, and there are 16 cups in a gallon. So, the cost of the sorbet per cup is $16.00 / 16 = $1.00 per cup.
- Since there are 67.6 ounces of soda, and 1 liter is approximately 33.8 ounces, Rafael needs 67.6 / 33.8 = 2 liters of soda. So, the cost of the soda per cup is $3.00 / 2 = $1.50 per cup.
Now, let's calculate the total cost per cup by adding the costs of the sorbet and the soda: $1.00 + $1.50 = $2.50 per cup.
Finally, to find the minimum price per cup that would give Rafael a $10 profit, we add the desired profit to the total cost: $2.50 + $10.00 = $12.50 per cup.
Therefore, Rafael should charge a minimum of $12.50 per cup of punch to make a $10 profit.