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Work Shown:
Note in step 2, I factored each number in the square root to pull out the largest perfect square factor. From there, I used the rule that to break up the roots.
There are 122,100 public school teachers in Ohio and Ohio has a population of 11.6 million people. Illinois has a population of 12.9 million people. If the number of public school teachers per capita in Illinois was proportional to that of Ohio, how many public school teachers would we expect Illinois to have?
This problem uses proportionality or the relationship between two values. Typically, proportions are expressed as fractions. So, we can set this up as
and we can use this to express both of our values. So, for Ohio, we have
and for Illinois we have
. Now, because they are proportional, we can set them equal to each other and we get
. Now we can cross multiply to get
. To get the
alone on one side, we divide by
and we get 124,662.931034, which is about equal to 124,663.
Therefore, we expect Illinois to have 124,663 public school teachers