Question

Dana can fill 31 glasses in 3 minutes. Which two proportions below could be solved for how many glasses she can fill in 45 minutes?

1) 31 glasses / 3 minutes = x glasses / 45 minutes
2) 31 glasses / 3 minutes = 45 minutes / x glasses
3) 31 glasses / x minutes = 45 glasses / 3 minutes
4) 31 glasses / 45 minutes = x glasses / 3 minutes

Answer 1

Using proportions, we find that Dana can fill 465 glasses in 45 minutes. Options 1 and 4 in the question correctly represent the proportions that can be used to solve this problem.

Step-by-step explanation:

The question asked by the student involves finding the rate at which Dana can fill glasses in a given amount of time (45 minutes), using the information that she can fill 31 glasses in 3 minutes. To solve this, we will use proportions. Of the given options, the following two are correct:

1. 31 glasses / 3 minutes = x glasses / 45 minutes
2. 31 glasses / 45 minutes = x glasses / 3 minutes

Both proportions equate the rate of filling glasses to find out how many glasses Dana can fill in 45 minutes. To solve this, you would cross-multiply and divide as needed.

For example, using the first proportion, the calculation would be:

31 glasses / 3 minutes = x glasses / 45 minutes

3 minutes * x glasses = 31 glasses * 45 minutes

x = (31 glasses * 45 minutes) / 3 minutes

x = 465 glasses

Therefore, Dana can fill 465 glasses in 45 minutes.