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This appears to be a mathematical problem from a Japanese textbook, with some work already done on it. Let me transcribe and analyze the problem to help you with the solution.

From what I can see, it seems like a question involving profit maximization or a pricing strategy, likely modeled by a quadratic equation based on the product's price and quantity sold.

I'll now transcribe and work on the equations provided.

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1. The problem refers to maximizing profits by adjusting the price of a product, \( A \). It involves calculating the price increase that would result in a profit exceeding a certain threshold (100 yen per unit).

- It looks like an equation related to sales price (denoted \( x \)) and the number of units sold.
- There is a quadratic expression in one section.

In the user-provided solution, we see the following expression written:
\[
(300 - x)(x + 200) = 0
\]

This can be expanded and solved as follows:
\[
300x + 200x - x^2 - 60000 = 0
\]
Simplifying:
\[
x^2 - 500x + 60000 = 0
\]

This is a quadratic equation, and we can solve it using the quadratic formula:
\[
x = \frac{-(-500) \pm \sqrt{(-500)^2 - 4(1)(60000)}}{2(1)}
\]
\[
x = \frac{500 \pm \sqrt{250000 - 240000}}{2}
\]
\[
x = \frac{500 \pm \sqrt{10000}}{2}
\]
\[
x = \frac{500 \pm 100}{2}
\]
Thus, the two solutions are:
\[
x = \frac{500 + 100}{2} = 300
\]
\[
x = \frac{500 - 100}{2} = 200
\]

The problem asks for a solution where the price exceeds a certain amount. The answer should be interpreted according to the constraints set in the problem.

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Do you want more detailed steps or clarifications for any part of the solution? Here are some related questions to help you understand the topic better:

1. What is the general form of a quadratic equation, and how do we solve it?
2. How do changes in price affect revenue and profit in pricing models?
3. How does the quadratic formula work for different types of problems?
4. What does maximizing profit mean in terms of quadratic equations?
5. How can you check if your solution to a quadratic equation is correct?

**Tip**: Always double-check your work by substituting the solution back into the original equation to verify that it holds true.

Solve the quadratic equation involving profit maximization related to a product's price and sales.

Learn how to solve a quadratic equation problem involving maximizing profits based on price and sales. This problem covers the quadratic equation formula, profit functions, and algebraic methods. Suitable for high school students in Grades 10-12.

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