# A health department estimates that 8 vials of malaria serum will treat 100 people. At this rate, how many vials are required to treat 175 people?

Mar 28, 2018

$14$

#### Explanation:

$\text{using "color(blue)"proportion}$

$100 \text{ people "to8" vials}$

$175 \text{ people "to8/1xx175/100=14" vials}$

Mar 28, 2018

$14$ vials

#### Explanation:

We can solve this using direct proportion. For direct proportion we have:

$y \propto k x$

Where $k$ is the constant of variation. To find $k$:

We know 8 vials will treat 100 people.So:

$8 = k 100$

Divide by 100:

$k = \frac{8}{100} = \frac{2}{25}$

$\therefore$

$y \propto \frac{2}{25} x$

Plugging in $x = 175$

$y = \frac{2}{25} \left(175\right) = 14$

$14$ vials are needed.