What is 482 students to 20 teachers?

10 teachers to 241 students

Step-by-step explanation:

Number of students  = 482

Number of teachers  = 20

Unknown:

ratio of students to teachers = ?

Solution:

To find the ratio:

     Number of students :  Number of teachers

                  482               :           20

Reduce to the smallest value, divide by 2;

                  241                 :           10

In the class there are 10 teachers to 241 students

we have three similar triangles, because each has a right angle and shares an angle.   let's write the angles in order: opposite to short leg, long leg, hypotenuse.

cab similar to bad similar to cbd

or as ratios,

ca: ab: cb = ba: ad: bd = cb: bd: cd

we also know

ac = ad + cd

(ad+cd): ab: cb = ba: ad: bd = cb: bd: cd

(ad+cd)/cb=cb/cd

we have cb=6, ad=5 and seek x=cd.

we reject the negative root and conclude x=4

answer: 4