https://file.aiquickdraw.com/mathbot/file/1729885762123cwymhey2.jpg

The equation given in the problem is:

\[
12.50h + 30.75 = 10h + 40.75
\]

This represents when the cost of making the vase is the same for both art studios. Let's analyze the options:

- **A. The values 12.50 and 10 are coefficients.**

  **True.** In this equation, 12.50 and 10 are multiplied by the variable \(h\) (hours), meaning they are coefficients.

- **B. Each side of the equation contains 1 factor.**

  **False.** A factor is something being multiplied as a whole (like a term in parentheses), but here there are two terms on both sides of the equation.

- **C. Each side of the equation contains 1 term.**

  **False.** The left side of the equation has two terms: \(12.50h\) and \(30.75\), while the right side has \(10h\) and \(40.75\).

- **D. The values 12.50 and 10 are constants.**

  **False.** Constants are values that do not change, like 30.75 and 40.75. The values 12.50 and 10 are multiplied by the variable \(h\), so they are coefficients, not constants.

Therefore, the correct answer is **A. The values 12.50 and 10 are coefficients.**

Would you like more details or have any further questions?

Here are 5 related questions to deepen your understanding:

1. How do you solve the equation \(12.50h + 30.75 = 10h + 40.75\) for \(h\)?
2. What is the significance of the coefficients in the context of this problem?
3. How can we interpret the constants 30.75 and 40.75 in terms of the art studios' pricing?
4. What does it mean for two equations to represent the same total cost?
5. How would the equation change if Art Studio A increased its per-hour rate?

**Tip:** In an equation, the **coefficient** is the number that multiplies a variable, while a **constant** is a standalone number without a variable.

Which statement is TRUE about the equation: 12.50h + 30.75 = 10h + 40.75?

Understand how to solve and analyze the linear equation 12.50h + 30.75 = 10h + 40.75, identifying coefficients and constants. This algebra problem is suitable for Grade 8 students.

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