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

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Answer 1 · 2016-10-05T08:49:22

$96$ $96$ students were surveyed.

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

$60$ $60$ students were found to have liked food

i.e. the ratio was found to be $\frac{60}{?}$ $60/color(red)?$

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

Hence, $\frac{60}{?} = \frac{5}{8}$ $60/color(red)?=5/8$

or $? \times 5 = 60 \times 8$ $color(red)?xx5=60xx8$

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

= $12xx8=96$

So $96$ students were surveyed.

Answer 2 · 2016-10-05T11:42:34

$96$ students surveyed.

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