ratio math question

Question

A total of 1 200 students attend Top View High School.
The ratio of teachers to students is l:30.
(i) How many teachers are there at the school? 

 

Two-fifths of the students own personal computers.
(ii) How many students do NOT own personal computers? 

Thirty percent of the students who own personal computers also own play stations.
(i)i) What fraction of the students in the school own play stations?
   

Express your answer in its lowest terms. 

Answer 1

I) Ratio of teachers to students = 1/30

 

Number of students at school = 1200

 

Number of teachers at school = (ratio of teachers/students)*(number of students)

                                            = (1/30)*(1200)

                                            = 40 teachers at school

 

ii)  2/5 of students own personal computers

 

Therefore, 1 - 2/5 or 5/5 - 2/5 = 3/5 of students do NOT own personal computers

 

Number of students who do NOT own personal computers = (3/5) * (1200)

 

                                                                                    =  720 students w/o computers

 

iii) 30% of students who own personal computers also own play stations. 

What fraction of the students own play stations?

 

So how many students own personal computers?

 

Students with computers = (2/5) * (1200)

                                     = 480 students own computers

 

Students with play stations = 30% of students with computers

                                        = (0.30) * (480)

                                        = 144 students have play stations

 

Fraction of students with play stations = 144/1200

                                                        = 144:1200 

                                                         = 12:100  (divide each side by 12)

                                                         = 6:50   (divide each side by 2)

                                                         = 3:25 ratio of students in school who own play stations