A sample of 125 students from a school shows that 85 students prefer to work by themselves. If the school has 1275 students, how many prefer to work in groups?

Question

I really need to know how to do this step by step.

Answer 1

"A sample" means that some, but not all, of the students were asked what they prefer.

 

Of the 125 students who were asked, 85 said "work alone."  That means that 40 of them must have said, "work in groups" (must assume only two possible answers).

 

Now, we must assume that the same rate (that is, the same ratio) applies to the total 1275 students.  Let's call the estimated total number of students who prefer to work in groups 'x.'   (NOTE: the question asks, "how many prefer to work in groups?")

 

We want the same "rate":

   40 per 125   =   x per 1275

    40/125  =  x/1275

     x = (40/125)*1275       [you could also cross-multiply]

     x = 408

 

This solution involves a proportion (two ratios set equal).  It also has a 'trick' -- mentioning work alone, but asking for work in groups.  Also, be sure the number of students is an integer.