Question

Out of the 860 students, 43 were out sick. What percent of the student population is ill?

Answer 1

To express a number as a percentage, you need to write it as a ratio with denominator 100.

We know that ratios have different forms they can be written into, for example, all the following are equivalent:

$\cfrac{3}{7} = \cfrac{30}{70} = \cfrac{9}{21} = \cfrac{15}{35} = \ldots$

So, since 43 students out of 860 are sick, the ratio of sick students is

$\cfrac{43}{860}$

and we want to express this as a ratio with denominator 100, so we have

$\cfrac{43}{860} = \cfrac{x}{100}$

So, if we solve for x, we have

$x = \cfrac{43\cdot 100}{860} = \cfrac{4300}{860} = 5$

So, 5% of students is sick.