Solve this: "Pencil + notebook = 100 yen". If pencil is 40 yen cheaper than a notebook, What is the price of a pencil?

Image: /twitter/2qnc_

Recently there was a game show in Japan asking this math question to an artist when she gave the wrong answer. Many netizens were shocked by the real answer and they still don't understand how the price of the pencil is 30 yen, most of them get the answer 60 yen.

まって本気で60円以外考えられないって言うか理由説明されても訳が分からないイライラする教えて pic.twitter.com/lAV0x0QuV5
— らびりん (@2qnc_) December 3, 2023

Pencil and Notebook Problem Puzzles Economists

In a recent study, economists have been grappling with a perplexing problem: the pencil and notebook paradox. The problem, which has been around for centuries, is as follows:

A pencil and a notebook cost 100 yen.

The pencil is 40 yen cheaper than the notebook.

How much does each item cost?

This seemingly simple problem has proven to be quite challenging to solve. Economists have come up with a variety of solutions, but none of them have been universally accepted.

One approach is to use algebra to solve for the unknown variables. Let x be the price of the notebook and y be the price of the pencil. We can then set up the following equations:

x + y = 100 y = x - 40

Solving for x and y, we get:

x = 70 y = 30

Therefore, the notebook costs 70 yen and the pencil costs 30 yen.

However, this solution is not without its critics. Some economists argue that the problem is too unrealistic, as it assumes that the pencil and notebook are always sold together. They argue that the prices of the two items should be determined independently of each other.

Another approach is to use game theory to solve the problem. Game theory is a branch of mathematics that deals with strategic decision-making. In the context of the pencil and notebook problem, the goal is to find the equilibrium prices for the two items.

An equilibrium price is a price at which there is no incentive for either the buyer or the seller to change their price. In other words, it is a price that is mutually acceptable to both parties.

Using game theory, economists have shown that there are multiple equilibrium prices for the pencil and notebook problem. This means that there is no single "correct" answer to the problem.

The pencil and notebook problem is a reminder that economics is a complex and nuanced field. There are often multiple ways to approach a problem, and there is no single "right" answer.