Are You Economical With Pizzas?

We know that the ratio of the areas of similar triangles is related to the ratio of it's sides in the following way: $\dfrac{\text{ar(triangle 1)}}{\text{ar(triangle 2)}} = \text{ratio of the sides}^2$

Thus, the area of the small pizza to the area of the large pizza would be: $\begin{aligned} \dfrac{\text{ar(small pizza)}}{\text{ar(large pizza)}} &= \left(\dfrac 56\right)^2 &=\dfrac{25}{36} \end{aligned}$

So, if Sandeep buys:

• $3$ small pizzas, the resulting area would be: $3\times 25x=75x$ .

• $2$ large pizzas, the resulting area would be: $2\times 36x=72x$ .

• $1$ large and $1$ small pizza, the resulting area would be: $25x+36x=61x$ .

Thus, the most economical choice would be to buy $3$ small pizzas.

I imagine that small pizza is 5 and large is 6 (Just numbers which indicate area). When I choose one of these option: 1 Large pizza and 1 Small pizza. 11 for 5$ So you get 2,2 per $. Now 2 large pizzas. 12 for 6 $. So 2 per 1 $, that means it is worse that opion 1. 3 small pizza is 15 per 6 $ which is 2,5 per 1$. 2,2 > 2 < 2,5 , so that mean that 3 small pizza is best opinion.

Sorry for my bad english or weird solution.

I think this is the normal approach... Let the angle of each slice be 10°, and let the radii of small and large slice be 5 and 6 respectively.

The area of a small slice is The area of a big slice is

Since 3 small slices cost the same as 2 big slices ($6), and the area of 3 small slices is slightly larger than 2 big slices: buying 3 small slices is more economical than 2 big slices.