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The problem is about a businessman who wants to know how many products need to be sold to earn a profit of Rp 100,000, given the profit function \( f(x) = 4x + 8 \) where \( x \) is the number of products sold and \( f(x) \) is the profit in thousands of Rupiah.

To find out how many products need to be sold to achieve a profit of Rp 100,000, we first need to convert the desired profit into the same units used in the function, i.e., thousands of Rupiah. Thus, \( f(x) = 100 \) (because 100,000 Rupiah equals 100 thousand Rupiah).

Now, we set up the equation:
\[ f(x) = 4x + 8 = 100 \]

Next, we'll solve for \( x \) to find the number of products:
\[ 4x + 8 = 100 \]
\[ 4x = 100 - 8 \]
\[ 4x = 92 \]
\[ x = \frac{92}{4} \]
\[ x = 23 \]

Therefore, the businessman needs to sell 23 products to achieve a profit of Rp 100,000.

Would you like more details on this solution, or do you have any other questions?

Here are some related questions you might find interesting:
1. What would the profit be if 50 products were sold?
2. How would the profit change if the profit function was modified to \( f(x) = 5x + 8 \)?
3. What is the minimum number of products that need to be sold to break even?
4. How does changing the constant term in the profit function from 8 to 10 affect the break-even point?
5. Can you determine the inverse function of \( f(x) \) and explain how it could be used in different scenarios?

Tip: When dealing with profit functions, it's crucial to maintain consistent units throughout your calculations to avoid errors.

A businessman has a formula to calculate the daily profit from his product, which is f(x) = 4x + 8, where x is the number of products sold, and f(x) is the profit in thousand Rupiah. One day, the businessman wants to know how many products he must sell to earn a profit of Rp 100,000. Determine how many products need to be sold by using the inverse function!

Learn how to determine the number of products a businessman needs to sell to earn Rp 100,000, using the profit function f(x) = 4x + 8 and its inverse. This math problem involves algebraic concepts such as inverse functions and linear equations, making it suitable for students in Grades 9-11.

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