the ratio of teachers to students is 1:10. If 447 more students enrolled, what was the total number of students and teachers

Question

the ratio of teachers to students if 1:10. 447 more students enrolled last year. If the number of students this year does not increase, how many teachers? how many students?

Answer 1

For every 1 teacher, there are 10 students.  

Assuming there are are 447 students this would be a probability question.

 

Therefore you can set the ratios equal to each other where x = the number of teachers.

 

1/10 = x/447 

 

So we isolate the x by multiplying each side of the equation to 447

 

(1/10) * 447 = (x/447) * 447

447/10 = x

44.7 = x

 

We then round this answer to the nearest whole number, since we can't have .7 of a teacher.

 

45 = x = # of teachers.

 

 

If we are assuming number of students enrolled is y + 447 because of " 447 MORE students enrolled last year", then, 

 

1/10 = x/(y+447)

 

Solve for x for # of teachers, and

solve for y for # of students.

Isolate each variable..

 

x = (1/10) x (y+447)

   = (y+447)/10

 

for y:

 

1/10 = x/(y+447)  (cross multiply)

 /x        /x           

(1/10)/x = 1(y+447)

 

10x = y+447

-447      -447

 

10x-447 = y