1. Set up the equation:
   • Fixed cost: $120
   • Cost per student:$2.50
   • Total cost: $325
     The equation representing the total cost is:
     \(120 + 2.5x = 325\)
     where x is the number of students.

2.Solve for x:

Subtract 120 from both sides:

\(2.5x= 325−120\)

\(2.5x= 205\)

Divide both sides by 2.5:

\(x= 82\)

Supplemental Knowledge

Linear equations are fundamental in algebra and are used to find unknown values by establishing relationships between different quantities. They often take the form \(ax + b = c\), where a, b, and c are constants, and x is the variable to be solved.

Key Concepts:

1. Setting Up the Equation:

Identify the fixed cost (constant term) and the variable cost (coefficient of the variable).

Formulate an equation that represents the total cost in terms of the number of students.

2. Solving Linear Equations:

Isolate the variable on one side of the equation by performing inverse operations.

Simplify step-by-step to find the value of the variable.

Concepts to Actions

Budget for events or planning expenses when organizing parties. A party might involve renting the venue at a fixed fee and charging per-person for food and activities - knowing how to set up and solve linear equations helps manage budget more effectively.

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