Math Problem Statement

A restaurant has benches and chairs arranged around dining tables. The restaurant has 3 times as many chairs as benches. The restaurant has 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 arranged around dining tables? Responses x = 3 y y = 34 + x x = 3 y y = 34 − − x y = 3 x y = 34 − − x

Solution

We are given that:

  1. The restaurant has 3 times as many chairs as benches.
  2. There are 34 more chairs than benches.

Let:

  • xx represent the number of benches.
  • yy represent the number of chairs.

First Equation:

  • The restaurant has 3 times as many chairs as benches, so: y=3xy = 3x

Second Equation:

  • There are 34 more chairs than benches, so: y=x+34y = x + 34

Thus, the system of equations that represents the situation is:

y &= 3x \\ y &= x + 34 \end{aligned}$$ So, the correct system of equations is: **$$y = 3x \quad \text{and} \quad y = x + 34$$** ### Tip: When two conditions are given, it's always helpful to translate them into separate equations, then solve the system. Do you have any questions or would you like a detailed solution for finding $$x$$ and $$y$$? Here are 5 related questions: 1. How do you solve a system of linear equations with substitution? 2. Can a system of equations have more than one solution? 3. How do you graphically represent a system of equations? 4. What does it mean when a system of equations is inconsistent? 5. How can you check the solution of a system of equations? Tip: Always check your final solution by substituting it back into the original equations.

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Math Problem Analysis

Mathematical Concepts

Algebra
Linear Equations
Systems of Equations

Formulas

y = 3x
y = x + 34

Theorems

Substitution Method
System of Linear Equations

Suitable Grade Level

Grades 7-8