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.