DC CAPE Geometry Modeling with Geometry. Practice it free.

Set up the proportion $\dfrac{x\text{ people}}{1\text{ square mile}} = \dfrac{37{,}800\text{ people}}{84\text{ square miles}}\textsf{.}$ Cross-multiplying gives $84x = 37{,}800\textsf{,}$ so $x = 450\text{ people per mile}^{2}\textsf{.}$

Set up the proportion $\dfrac{12\text{ kilograms}}{1\text{ cubic meter}} = \dfrac{540\text{ kilograms}}{x\text{ cubic meters}}\textsf{.}$ Cross-multiplying gives $12x = 540\textsf{,}$ so $x = 45\text{ m}^{3}\textsf{.}$

Set up the proportion $\dfrac{1{,}250\text{ people}}{1\text{ square mile}} = \dfrac{x\text{ people}}{48\text{ square miles}}\textsf{.}$ Cross-multiplying gives $x = 1{,}250 \times 48 = 60{,}000\text{ people}\textsf{.}$

Set up the proportion $\dfrac{18\text{ cattle}}{1\text{ acre}} = \dfrac{414\text{ cattle}}{x\text{ acres}}\textsf{.}$ Cross-multiplying gives $18x = 414\textsf{,}$ so $x = 23\text{ acres}\textsf{.}$

Set up the proportion $\dfrac{35\text{ picnic tables}}{1\text{ acre}} = \dfrac{x\text{ picnic tables}}{24\text{ acres}}\textsf{.}$ Cross-multiplying gives $x = 35 \times 24 = 840\text{ picnic tables}\textsf{.}$

Set up the proportion $\dfrac{8\text{ pounds}}{1\text{ cubic foot}} = \dfrac{1{,}920\text{ pounds}}{x\text{ cubic feet}}\textsf{.}$ Cross-multiplying gives $8x = 1{,}920\textsf{,}$ so $x = 240\text{ ft}^{3}\textsf{.}$

Set up the proportion $\dfrac{x\text{ packages}}{1\text{ cubic foot}} = \dfrac{4{,}800\text{ packages}}{160\text{ cubic feet}}\textsf{.}$ Cross-multiplying gives $160x = 4{,}800\textsf{,}$ so $x = 30\text{ packages per ft}^{3}\textsf{.}$

Set up the proportion $\dfrac{25\text{ BTUs}}{1\text{ cubic foot}} = \dfrac{x\text{ BTUs}}{120\text{ cubic feet}}\textsf{.}$ Cross-multiplying gives $x = 25 \times 120 = 3{,}000\text{ BTUs}\textsf{.}$