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The problem states that a restaurant has benches and chairs, with:

1. The number of chairs being 3 times the number of benches.
2. There are 34 more chairs than benches.

Let:
- \( x \) be the number of benches.
- \( y \) be the number of chairs.

From the first point, we can express the number of chairs as:
\[ y = 3x \]

From the second point, the number of chairs is also 34 more than the number of benches:
\[ y = x + 34 \]

Thus, the system of equations is:
\[
\begin{aligned}
y &= 3x \\
y &= x + 34
\end{aligned}
\]

The correct option is the third one:
\[
y = 3x \quad \text{and} \quad y = 34 + x
\]

Would you like more details or have any questions?

Here are 5 related questions:
1. How would you solve this system of equations to find the values of \( x \) and \( y \)?
2. What are the solutions for the number of benches and chairs based on the system of equations?
3. How do systems of linear equations help solve real-world problems like this one?
4. What method could you use to verify the solution to this system of equations?
5. How would the system of equations change if there were 40 more chairs than benches?

**Tip:** When solving systems of equations, substitution is often useful when one equation is already solved for a variable!

A restaurant has benches and chairs arranged around dining tables. The restaurant has 3 times as many chairs as benches and 34 more chairs than benches. Which system of equations can be used to determine the number of benches (x) and chairs (y) that the restaurant has?

Learn how to solve a system of equations problem involving the number of benches and chairs in a restaurant, where the number of chairs is 3 times the number of benches, and there are 34 more chairs than benches. Suitable for students in Grades 7-9.

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