https://file.aiquickdraw.com/mathbot/file/1727443237030l496ss5a.jpg

The question asks which situation can be represented by the equation:

\[
18x = 19 + 12x
\]

Let's break down the equation first. Rearranging the terms:

\[
18x - 12x = 19 \implies 6x = 19 \implies x = \frac{19}{6} \approx 3.17
\]

This means that $x$ represents a quantity where the difference between two varying rates becomes equal after approximately 3.17 units of time or effort.

Now, let's analyze each option in the image:

**Option A:**  
Krystal reads 12 pages per hour, and Jondo reads 18 pages per hour. The equation would represent a situation where the total pages read by Krystal and Jondo are compared. However, the equation does not directly fit the situation where one person's rate has a constant or starting value (like the 19 in the equation). Thus, **Option A does not match** the equation.

**Option B:**  
Krystal paid a deposit of $19 and $18 per hour to rent a dining room, while Jondo pays $12 per hour. This situation has a fixed amount ($19) and rates ($18 and $12), making it the most consistent with the equation form $18x = 19 + 12x$. The $19 deposit corresponds to the constant, and the hourly rates of $18 and $12 match the coefficients of $x$. Thus, **Option B fits the equation**.

**Option C:**  
Krystal installs 12 tiles per hour, and Jondo installs 19 tiles per hour, but Jondo already started with 18 tiles installed. This is not represented by the equation since the constant term in the equation is 19, not 18, and the situation doesn't correspond to the relationship between the rates and the constant term. So, **Option C does not match**.

**Option D:**  
Krystal can make $18 per hour by tutoring, and Jondo can make $12 per hour, but Jondo already has $19. This may seem to fit, but the roles of the constant $19 and the hourly rates don't align well with the equation structure. So, **Option D also does not match**.

The correct answer is **Option B**.

Would you like any further details or explanation?

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Here are 5 related questions to explore:

1. How do we solve equations with variables on both sides, such as $18x = 19 + 12x$?
2. How can you distinguish between linear equations with and without a constant term?
3. What other real-life scenarios can be modeled by linear equations like this one?
4. What happens to the solution if both hourly rates (like $18 and $12) were equal?
5. How would the equation change if Jondo’s deposit or initial value were different?

**Tip:** When analyzing word problems, always identify constants, variables, and rates to match them with the algebraic equation.

Which situation can be represented by this equation? 18x = 19 + 12x

Learn how to solve the linear equation 18x = 19 + 12x and match it to real-life scenarios. This problem involves comparing hourly rates with a fixed cost, suitable for students in Grades 6-8.

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