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The problem describes two individuals, Trey and Ezra, spending the same amount of money at a restaurant.

- Trey bought 4 nuggets and gave a tip of 7.06.
- Ezra bought 6 nuggets and gave a tip of 2.

The equation you selected from the options is:

\[
4x + 7.06 = 6x + 2
\]

This equation represents the situation well. Here's the reasoning:

1. **Trey's cost**: Trey bought 4 nuggets. If the cost of one nugget is $x$, then the cost of 4 nuggets is $4x$. He also gave a tip of 7.06, so the total cost for Trey is $4x + 7.06$.

2. **Ezra's cost**: Ezra bought 6 nuggets, so his cost is $6x$, and he gave a tip of 2, making his total $6x + 2$.

Since both spent the same amount of money, the equation that equates their total costs is:

\[
4x + 7.06 = 6x + 2
\]

### Solving the equation:
\[
4x + 7.06 = 6x + 2
\]

Step 1: Subtract $4x$ from both sides:
\[
7.06 = 2x + 2
\]

Step 2: Subtract 2 from both sides:
\[
7.06 - 2 = 2x
\]
\[
5.06 = 2x
\]

Step 3: Divide both sides by 2:
\[
x = \frac{5.06}{2} = 2.53
\]

So, each nugget costs **$2.53**.

Would you like further details on this solution? Here are five related questions to explore the topic further:

1. How would the equation change if Trey gave a smaller tip?
2. What if both Trey and Ezra gave the same tip? How would the equation look?
3. How can you verify the solution by substituting $x = 2.53$ back into the original equation?
4. How could this type of problem be extended to involve multiple items, not just nuggets?
5. What is the general process for solving linear equations involving multiple variables?

**Tip**: Always check your solution by plugging the value back into the original equation to ensure both sides are equal.

Trey and Ezra spent the same amount of money at a restaurant. Trey bought 4 nuggets and gave a tip of 7.06, while Ezra bought 6 nuggets and gave a tip of 2. What equation would represent this situation, and how much did each nugget cost?

Solve a real-world linear equation problem where Trey and Ezra spend the same amount of money at a restaurant with different tips and number of nuggets. Learn how to find the cost of each nugget using algebra. Suitable for Grades 8-10.

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