Let's first determine the fraction of students in the class that have red backpacks. We can then convert the fraction to a percentage.

The question tells us that 6 out of 24 students have red backpacks. This is equal to six over twenty-four:

We can reduce the fraction by removing a common factor.

The percentage that is equivalent to is 25 percent, or .

Therefore,  is the correct answer. 

We know that there are the same proportions of cookies in both the small and large boxes.

Let's start by looking at the small box. We know that there are 3 vanilla and 2 chocolate cookies, or a ratio of .

In the large box, we know there are 6 chocolate cookies. If is the number of vanilla cookies, then the ratio in the large box is .

The ratios must be equal.

Cross-multiply and solve for .

If there is a room of 21 people in which the ratio of men to women is , that means that there are 9 men and 12 women in the room. 

If 2 men leave the room, there will be 7 men and 12 women in the room, with a total of 19 people. 

Therefore, the proportion of the men in the room is . 

If the ratio of boys to girls in a class is , that means that for every 3 students, 1 is a boy.

Looking at the ratio, we see that there is one boy for every two girls. In a group of three students, you would have one boy and two girls.

We can write the fraction of boys as the number of boys over the number of students in the group.

If it takes Linda 6 minutes to complete a multiple choice question, then she will complete  questions in 30 minutes. 

Therefore, Linda will complete 5 out of 10 questions in half an hour, or 50%. 

If  store sells  pies, and typically  of the pies that are sold are blueberry, that means that  of the pies sold were probably blueberry. 

Given that  of  is , it follows that  of  is . 

Therefore,  is the correct answer.

Given that the ratio of rabbits to guinea pigs to hamsters in a pet store is , each number should be 4 times greater if there are 12 rabbits. This is because 3 times 4 is 12. 

Therefore, we can transform the of rabbits to guinea pigs to hamsters into . 

Therefore, there are 16 hamsters. 

To simplify, you find a common factor for both the numerator and denominator and divide them both by that value.  

Both  and  have a common factor of .  

This gives us,

 .

In order to solve this problem, you would set up a direct proportion:

To make the process even simpler, you could first reduce the first fraction in this direct proportion. The fraction was reduced to simplest form by dividing both the numerator and the denominator by 8, the greatest common factor or the GCF.

Divide both sides by the coefficient of x, which is 8:

The proportion for the problem will be,

.  

You then cross multiple to get 

.  

To find , you divide both sides by  to get

Therefore