# How do you use proportions to solve percent equations?

Jun 22, 2018

See example

#### Explanation:

Using an example:

Suppose we had a big animal sanctuary for cats and dogs.

We had say 30 cats and 50 dogs

So by proportion we have:

$\textcolor{b l u e}{\text{Using format type 1}}$

$\text{cats : dogs } \to 30 : 50 \to 3 : 5$ as ratio (proportions)

But for $3 : 5$ we have 3 parts in combination with 5 parts giving a proportion total of $3 + 5 = 8$

Converting this to fractions and hence percentage

Cats
=3/(3+5)=3/8 -> 3/8xx100% =color(white)("ddd") 37.5%" of the whole"
Dogs
=5/(3+5)=5/8->5/8xx100% = color(white)("ddd")ul(62.5%" of the whole"
color(white)("ddddddddddddddddd")"Added up "->100.0%" all of the whole"

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

$\textcolor{b l u e}{\text{Using format type 2 - Fraction format}}$

("cats")/("dogs") ->30/50 ->3/5 larr" This is NOT a fraction of the whole"

Again we have

("cats")/("cats + dogs")->3/(3+5)xx100% = 37.5%" of the whole"

$\left(\text{dogs")/("cats + dogs")->5/(3+5)xx100% =ul( 62.5%" of the whole}\right)$
color(white)("ddddddddddddddddddddddddddd")100.0%