Answer
The large pizza will be a better buy as its price per square inch is less than that of a medium pizza.
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\[\frac{1}{2}\times 14\text{ in}\text{.}=7\text{ in}\text{.}\], or \[7\text{inches}\]
Radius of the medium pizza is\[\frac{1}{2}\times 7\text{ in}\text{.}=3.5\text{ in}\text{.}\], or\[3.5\text{inches}\].
Compute the areas (A) of the pizzas as follows:
For large pizza:
\[\begin{align}
& A=\pi {{r}^{2}} \\
& =\pi {{\left( 7 \right)}^{2}} \\
& =\text{49}\pi \text{ in}{{\text{.}}^{\text{2}}} \\
& \approx 153.9\text{ in}{{\text{.}}^{\text{2}}}
\end{align}\]
For medium pizza:
\[\begin{align}
& A=\pi {{r}^{2}} \\
& =\pi {{\left( \frac{7}{2}\text{ in}. \right)}^{2}} \\
& =\frac{49}{4}\pi \text{ in}{{\text{.}}^{\text{2}}} \\
& \approx 38.5\text{ in}{{\text{.}}^{\text{2}}}
\end{align}\]
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:
\[\begin{align}
& \text{Price or large pizza}=\frac{\$12}{\text{153}\text{.9in}{{\text{.}}^{\text{2}}}}\\&\approx\frac{\$0.08}{\text{in}{{\text{.}}^{\text{2}}}}\end{align}\]
\[\begin{align}
& \text{Price for medium pizza}=\frac{\$5}{\text{38}\text{.4in}{{\text{.}}^{\text{2}}}}\\&\approx\frac{\$0.13}{\text{in}{{\text{.}}^{\text{2}}}}\end{align}\]
Since, the price per square inch for large pizza is $0.08 per inch is lesser than the medium pizza whose price is $0.13 per square inch. Hence, 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 a medium pizza.
