How do you use proportions to solve percent equations?

1 Answer
Jun 22, 2018

Answer:

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:

#color(blue)("Using format type 1")#

#"cats : dogs " ->30:50->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"#

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

#color(blue)("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"#

#("dogs")/("cats + dogs")->5/(3+5)xx100% =ul( 62.5%" of the whole")#
#color(white)("ddddddddddddddddddddddddddd")100.0%#