https://file.aiquickdraw.com/mathbot/file/1726253710677227ye5kw.jpg

Let's analyze the problem given in the image and solve it.

### Problem Breakdown:
- Samantha bought **m** mugs for **$3.50** each.
- She also bought **m** plates for **$4** each.
- She used a **$12 discount** coupon, and the total cost was **$213**.

The equation provided to find the number of mugs is:

\[
3.5m + 4m - 12 = 213
\]

### Steps to solve:
1. Combine like terms on the left-hand side of the equation:

\[
(3.5m + 4m) = 7.5m
\]

So the equation becomes:

\[
7.5m - 12 = 213
\]

2. Add 12 to both sides to eliminate the constant on the left:

\[
7.5m = 213 + 12
\]
\[
7.5m = 225
\]

3. Now, divide both sides by 7.5 to isolate **m**:

\[
m = \frac{225}{7.5}
\]
\[
m = 30
\]

Thus, **Samantha bought 30 mugs**.

The correct answer is **C. 30 mugs**.

---

Would you like further details or clarifications on this solution?

### Related Questions:
1. If Samantha had used a $15 coupon instead of $12, how would the number of mugs change?
2. What would be the cost of mugs if she had purchased 40 instead?
3. How would the equation change if the price of plates was $5 each?
4. Can this equation be solved graphically? If so, how?
5. What if the total cost without any coupon was $250, how many mugs would she have bought?

### Tip:
Always check if terms in an equation can be simplified first to make solving easier.

Samantha bought m mugs for $3.50 each and the same number of plates for $4 each. She used a $12 discount coupon on the total cost and paid $213. How many mugs did Samantha buy from the store? Equation: 3.5m + 4m - 12 = 213

Learn how to solve a linear equation problem where Samantha buys mugs and plates using a discount. This problem involves basic algebra and solving for the variable m, representing the number of mugs she bought.

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