The student to teacher ratio is 19:1 at a local school and there is a total of 500 students and teachers. How many teachers and how many students are there.

I'm not sure how to begin to set this up since I have two unknowns and not only one.

s = number of students

19/20 = s/500

Cross multiply and solve for s.

The answer was 280

I thought it wasn’t a multiple choice question?

To solve this problem, you can start by assigning variables to the unknown quantities. Let's use "S" to represent the number of students and "T" to represent the number of teachers.

According to the information given, the student-to-teacher ratio is 19:1. This means that for every 19 students, there is 1 teacher.

Given that the total number of students and teachers is 500, we can write the following equation:

S + T = 500

Now, since the ratio of students to teachers is 19:1, we know that S divided by T is equal to 19.

S / T = 19

To find the values of S and T, we can solve these two equations simultaneously.

One way to do this is to isolate a variable in the first equation and substitute it into the second equation. Let's solve for S in terms of T in the first equation:

S = 500 - T

Now we can substitute this expression for S in the second equation:

(500 - T) / T = 19

Simplifying the equation:

500 - T = 19T

Combine like terms:

500 = 20T

Divide both sides by 20:

T = 500 / 20 = 25

Now that we know the value of T (the number of teachers), we can substitute it back into the first equation to find S (the number of students):

S + 25 = 500

S = 500 - 25 = 475

So, there are 475 students and 25 teachers at the school.

let the number of students be 19x

let the number of teachers be x

19x + x = 500
20x = 500
x = 25

There are 19(25) or 475 students
and 25 teachers

check:
total = 25+475 = 500
ratio = 475 : 25 = 19:1