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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

$\frac{Teachers}{Population}$ and we can use this to express both of our values. So, for Ohio, we have $\frac{122,100}{11,600,000}$ and for Illinois we have $\frac{x}{12,900,900}$ . Now, because they are proportional, we can set them equal to each other and we get $\frac{122,100}{11,600,00} = \frac{x}{12,900,000}$ . Now we can cross multiply to get $11,600,000x=1446090000000$ . To get the $x$ alone on one side, we divide by $11,600,000$ and we get 124,662.931034, which is about equal to 124,663.