Question

When surveyed, 5 out of every 8 students liked the food in the cafeteria. If 60 liked the food, how many were surveyed?

Answer 1

`96` students were surveyed.

Explanation:

In the survey of the `color(red)?` students having food in a cafeteria,

`60` students were found to have liked food

i.e. the ratio was found to be `60/color(red)?`

But this was `5` out of every `8`

Hence, `60/color(red)?=5/8`

or `color(red)?xx5=60xx8`

and `color(red)?=60xx8/5=12cancel(60)xx8/(1cancel5)`

= `12xx8=96`

So `96` students were surveyed.

Answer 2

`96`students surveyed.

Explanation:

5 students out of every 8 students asked liked the food.
60 students liked the food.

This tells us that 60 students represents 5 parts of the whole.
We can find out how many there are in 1 part.

`60div 5 = 12`

1 part is 12 students.
The whole is made up of 8 parts.

`8xx12 = 96` is the whole number of students surveyed.

Check:
`5/8 xx 96 = 60` students