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How much chicharrón can Jeff Bezos buy?

This is a calculation made by Sebastián Tobón when he was taking the course Numerical Methods for Partial Differential Equations (in 2020). The purpose was to encourage doing quick calculations (back-of-the-envelope) and having the size of some numbers (for example, 10¹²) in their heads. Here is the question I asked:

How much chicharrón (pork rinds) can Jeff Bezos buy?

Below is his answer.

Sebastián's answer

Suppose an average pig weighs 80 kg. If its muscle tissue constitutes 35% to 40% of its body weight, we can ge 30 kg of meat.

Jeff Bezos has a net worth of

\begin{equation*} JB = 115.7 \times 10^9 \text{ USD}\, . \end{equation*}

The price of 100 g of chicharrón is

\begin{equation*} 7000\text{ COP}\, \frac{1\text{ USD}}{3539.13\text{ COP}} = 1.978\text{ USD}\, . \end{equation*}

Jeff Bezos can therefore buy

\begin{equation*} \frac{115.7\times 10^9\text{ USD}}{\frac{1.978\text{ USD}}{100\text{ g}}} = 5.85\times 10^{12}\text{ g of chicharrón.} \end{equation*}

The total number of pigs in the world is 1×10⁹. This is equivalent to a total of

\begin{equation*} 1\times 10^9 \text{ heads} \times \frac{30\text{ kg}}{1\text{ head}} = 3\times 10^{13} \text{ g of chicharrón.} \end{equation*}

In order to buy all the pork rinds in the world, he must increase his net worth by 5.13.

The most expensive pigs in the world cost around 1000 USD, then

\begin{equation*} \frac{1000\text{ USD}}{\text{head}}\times 10^9\text{ heads} = 10^{12}\text{ USD}\, . \end{equation*}

On the other hand, he can buy 5.85 times the amount of pigs globally — the most expensive in the market. Therefore

it is more profitable for him to buy all the pigs in the world.


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