EXPLANATION:
We are given the ratios of obese to non-obese adults in two cities.
To simplify our calculations and explanations we shall assign variables to obese and non-obese adults as follows;
[tex]\begin{gathered} x=obese \\ y=non-obese \end{gathered}[/tex]That means the ratios for the two cities would be as shown below;
[tex]\begin{gathered} Evansville=x:y \\ Evansville=189:311 \end{gathered}[/tex][tex]\begin{gathered} Boulder=x:y \\ Boulder=16:109 \end{gathered}[/tex]With the given ratios we can now calculate the number out of the entire population which is represented by each variable.
This is shown below;
[tex]\begin{gathered} Evansville: \\ Total=358,676 \\ x=\frac{189}{(189+311)}\times358676 \end{gathered}[/tex][tex]\begin{gathered} x=\frac{189}{500}\times358676 \\ \end{gathered}[/tex][tex]x=135579.528[/tex]We can round this to the nearest whole number which is;
[tex]x\approx135,580[/tex]The value of y for Evansville would now be;
[tex]\begin{gathered} Total-x=y \\ 358676-135580=y \end{gathered}[/tex][tex]y=223,096[/tex]This means in Evansville, there are 135,580 obese adults and 223,096 non-obese adults. We shall now move on to Boulder;
[tex]\begin{gathered} Boulder: \\ Total=308,482 \\ x=\frac{16}{(16+109)}\times308482 \end{gathered}[/tex][tex]x=\frac{16}{125}\times308482[/tex][tex]x=39485.656[/tex]We will round this to the nearest whole number and that is;
[tex]x\approx39,486[/tex]The value of y in Boulder will now be;
[tex]\begin{gathered} Total-x=y \\ 308482-39486=y \end{gathered}[/tex][tex]y=268,996[/tex]With this result for Boulder, we can conclude that there are 39,486 obese adults and 268,996 non-obese adults in Boulder.
The number of obese people compared for both cities are;
[tex]\begin{gathered} Obese\text{ }people: \\ Evansville=135,580 \\ Boulder=39,486 \end{gathered}[/tex]The difference would be;
[tex]\begin{gathered} Difference=135580-39486 \\ Difference=96,094 \end{gathered}[/tex]ANSWER:
There were 96,094 more obese people in Evansville than in Boulder
