Question

6a) a total of 5000 students attend the st. catherine high school. The ratio of teachers to students 6:25.

i) how many teachers are there in the school?

b) a quarter of the students in the school owns i-phone classic 20.
(ii) how many students DO NOT own an i-phone classic 20?

c) 60% of the students who own an i-phone classic 20 also owns a samsung galaxy a80s.
(i) what fraction of the students in the school own samsung galaxy a80s?

Please show all working
thanks

Answer 1

a) (i) 1200

b) (ii) 3750

c) (i)
`(3)/(20)`

Explanation:

a) Total number of students = 5000

Ratio of teachers to students = 6 : 25

i) Number of teachers = ?

By the given ratio, we can let the number of teachers = 6
`x`

and we can let the number of students = 25
`x`

`25x = 5000\\\Rightarrow x = 200`

Therefore, number of teachers = 6
`*` 200 = 1200

b) A Quarter of the students own i-phone classic 20.

ii) Number of students who do not own an i-phone classic?

As per question statement,

Number of students who own i-phone classic 20 =
`(1)/(4)* 5000` = 1250

Number of students who do not own i-phone classic 20 = 5000 - 1250 = 3750

c) Number of students who own samsung galaxy a80s = 60% of students who own i-phone classic 20 =
`(60)/(100)* 1250` = 750

Fraction of students who own samsung galaxy a80s = Number of students having samsung a80s divided by total number of students

`(750)/(5000) = (3)/(20)`