Question

If a high school employs 9 teachers for every 80 ​students, how many students are in the school if it employs 216 ​teachers?

Answer 1

Answer: 1,920 students

Step-by-step explanation: To solve this problem, our first step is to write down the unit ratio that is involved. In this case, it's teachers/students.

Next, we set up a proportion based on the information given in the problem.

We know that the high school employs 9 teachers for every 80 students so we have 9/80 and we're asked how many students are in the high school if the high school employs 216 teachers so that's x/216.

Now we have the following proportion:

`(9)/(80) = (216)/(x)`

Notice that the 216 teachers must go on top in the second ratio because our unit ratio tells us that we put teachers over students.

Solving from here, we use the means extremes property to get 9x = 17,280. Dividing both sides by 9, we find that x is equal to 1,920.

Therefore, the school will have 1,920 students if the high school employs employs 216 teachers.