https://file.aiquickdraw.com/mathbot/file/1726799272672l4sblj28.jpg

Let me analyze the mathematical content of the image and interpret the equations to provide a detailed solution.

There are two equations presented:

1. $ 18x - 36 = 234 $
2. $ 9x + 36 = 81 $

The task is to determine which stories correspond to these equations, or if none of the options match.

### Part (a): $ 18x - 36 = 234 $

Let's solve the equation:
\[
18x - 36 = 234
\]
First, add 36 to both sides:
\[
18x = 270
\]
Now divide both sides by 18:
\[
x = 15
\]
So, the value of $ x $ is 15.

This equation seems to involve a charge of $18 per unit with a discount of $36, and the final cost is $234 after the discount.

- Option 1: If Camrie printed 2 banners, the total should be $ 18(2) - 36 = 36 - 36 = 0 $, which does not match $234. This option is incorrect.
- Option 2: Camrie printed 18 banners, the total would be $ 18(18) - 36 = 324 - 36 = 288 $, which does not match $234. This option is incorrect.
- Option 3: Camrie printed 36 banners, $ 18(36) - 36 = 648 - 36 = 612 $, also incorrect.
- Option 4: Camrie printed 15 banners, $ 18(15) - 36 = 270 - 36 = 234 $, which is correct.

Thus, the correct story for equation $ 18x - 36 = 234 $ is option 4.

### Part (b): $ 9x + 36 = 81 $

Now solving the second equation:
\[
9x + 36 = 81
\]
Subtract 36 from both sides:
\[
9x = 45
\]
Now divide by 9:
\[
x = 5
\]
So, $ x = 5 $.

This equation seems to involve a price of $9 per unit, with a total of $81, but there is an additional $36 added before the total.

- Option 1: If Adrian sold 9 shirts, his earnings are $ 9(9) + 36 = 81 + 36 = 117 $, which is not correct.
- Option 2: Adrian sold 5 shirts, $ 9(5) + 36 = 45 + 36 = 81 $, which is correct.
- Option 3: Adrian sold 9 shirts, $ 9(9) - 36 = 81 - 36 = 45 $, which is incorrect.
- Option 4: Adrian sold 5 shirts and incurred expenses, but this does not match the structure of the equation, so it is incorrect.

Thus, the correct story for equation $ 9x + 36 = 81 $ is option 2.

### Conclusion:
- For equation $ 18x - 36 = 234 $, the correct story is option 4.
- For equation $ 9x + 36 = 81 $, the correct story is option 2.

Would you like a more detailed breakdown of any part? Here are some related questions:

1. How would you solve similar equations with different constants?
2. Can you explain why some of the incorrect options don't match the equations?
3. What steps are involved in simplifying algebraic expressions like these?
4. How would the interpretation change if a term was subtracted instead of added?
5. How can you check your work after solving equations like these?

**Tip:** Always double-check the equation structure with real-life context (like sales or discounts) to ensure the story aligns properly with the math.

Select all of the stories that can be represented by the equations: 18x - 36 = 234 and 9x + 36 = 81.

Learn how to solve linear equations like 18x - 36 = 234 and 9x + 36 = 81, with real-world examples involving discounts and earnings. Detailed breakdowns and step-by-step solutions are provided for students in Grades 7-10.

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