word problem!!!!!!

Question

Mr. Carter offered to stay after school for an extra help session, and 2 of his 11 students stayed for the session. If there were 24 students that stayed for the help session, how many students does Mr. Carter teach throughout the day?

Answer 1

Let's first think about this question more abstractly. To start, let's call the number of students that stayed after school H, the number of students who are tutored per session T, the total number of students per session S, and the number of students Mr. Carter teaches throughout the day X. Let's next set up the proportion using these variables:

 

H/X = T/S

 

This proportion should make sense, because the assumption is that the ratio of students in a particular session (T/S) who stay for tutoring is true of the ratio of the total number of students who stay for tutoring to the total number of students Mr. Carter teaches throughout the day. In the prompt, we are told that H = 24, T = 2, and S = 11. Let's fill these values into the proportion and see what remains:

 

24/X = 2/11

 

We want to solve for X, so we need to find a way to get X by itself on one side of the equation. To do this, let's first multiply each side by X:

 

(24/X)*X = (2/11)*X

 

Which gives us:

 

24 = 2X/11

 

(Remember that 1/X times X = X/X =1)

 

Next, let's make 2X just X by dividing each side by 2 (which is also the same as multiplying by 1/2):

 

24*1/2 = (2X/11)*(1/2)

 

Which gives us:

 

12 = X/11

 

Now, the last step is to multiply each side by 11 to finally isolate the X:

 

12*11 = (X/11)*11

 

Which gives us:

 

12*11 = X

 

This is a very simple calculation that will give you the number of students Mr. Carter teaches throughout the day.