https://file.aiquickdraw.com/mathbot/file/1726499909399nhtfamct.jpg

The question asks which situation is best modeled by the equation:

\[
12x + 10 = 15x + 8
\]

### Analysis of the options:

1. **Option A:**
   - The hardware store sells wrenches for $10 each and a hammer for $12.
   - The discount store sells wrenches for $8 each and a hammer for $15.
   - The equation would represent balancing the total cost at each store, with $x$ being the number of wrenches purchased.
   - This situation could lead to an equation of this form since both terms on the left and right represent the total cost at the two stores, and you're balancing them.

2. **Option B:**
   - Joy jogged for 10 miles and cycled at 12 miles per hour for $x$ hours.
   - Hanna jogged for 8 miles and cycled at 15 miles per hour for $x$ hours.
   - This option involves distance and speed but isn't a cost equation, and it wouldn't produce an equation in the form $12x + 10 = 15x + 8$.

3. **Option C:**
   - Reginald assembled skateboards for $x$ hours and packed skates, while Shantel also worked for $x$ hours assembling and packing.
   - The situation involves time and tasks, but it doesn't fit the structure of the equation $12x + 10 = 15x + 8$ since the equation seems to model cost rather than time.

4. **Option D:**
   - Math quizzes have word problems worth 12 points and graphing problems worth 10 points. Science quizzes have lab problems worth 15 points and essay problems worth 8 points.
   - Here, the total points from both quizzes are compared, and this could produce an equation of this form, making it a strong candidate.

### Conclusion:
The correct situation modeled by the equation is **Option D**, as it compares the total number of points for math and science quizzes, balancing them through the given point structure.

Do you want any further details or clarifications?

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Here are 5 related questions:
1. How would the equation change if one store had a different hammer price?
2. Can you model a similar situation where the distance traveled by two people is equal?
3. What if the cost of the hammer were variable—how would that affect the equation in Option A?
4. How can you apply a system of equations to compare multiple quizzes with different grading systems?
5. Can you create a similar problem involving time and speed, like in Option B?

**Tip:** When creating equations, always ensure that each side of the equation corresponds to the same quantity being compared (like cost, distance, or points).

Which of the following situations is best modeled by the equation 12x + 10 = 15x + 8?

Explore how to model real-world situations using the linear equation 12x + 10 = 15x + 8. This problem compares costs and points, covering key algebraic concepts. Ideal for students in Grades 7-9.

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