Answer
The large pizza will be a better buy as its price per square inch is less than that of two small pizzas.
Work Step by Step
Out of the two given pizzas, the one with the low price per square inch will be better.
Radius of the large pizza is\[\frac{1}{2}\times 16\text{ in}\text{.}=8\text{ in}\text{.}\]or \[8\text{ inches}\] and of the medium pizza is\[\frac{1}{2}\times 10\text{ in}\text{.}=5\text{ in}\text{.}\]or \[5\text{ inches}\].
Compute the areas of the pizzas as follows:
For large pizza:
\[\begin{align}
& A=\pi {{r}^{2}} \\
& =\pi {{\left( 8 \right)}^{2}} \\
& =\text{64}\pi \text{ in}{{\text{.}}^{\text{2}}} \\
& \approx 201.05\text{ in}{{\text{.}}^{2}}
\end{align}\]
For small pizza:
\[\begin{align}
& A=\pi {{r}^{2}} \\
& =\pi {{(5\text{ in}\text{.})}^{2}} \\
& =25\pi \text{ in}{{.}^{2}} \\
& \approx 78.5\text{ in}{{.}^{2}}
\end{align}\]
For both the pizzas, the price per square inch of the pizza can be found out by dividing the price by the area of the pizza.
Compute the price per square inch as follows:
\[\begin{align}
& \text{Price for large pizza}=\frac{\$12}{201.05\text{in}{{\text{.}}^{\text{2}}}}\\&\approx\frac{\$0.060}{\text{in}{{\text{.}}^{\text{2}}}}\end{align}\]
\[\begin{align}
& \text{Price for small pizza}=\frac{\$5}{\text{78}\text{.5in}{{\text{.}}^{\text{2}}}}\\&\approx\frac{\$0.063}{\text{in}{{\text{.}}^{\text{2}}}}\end{align}\]
Since, the price per square inch for large pizza is \$0.060 per square inch which is lesser than the small pizza which is $0.063 per square inch. It will be a better buy.
Hence, the large pizza will be a better buy as its price per square inch is less than that of two small pizzas.
