Problem 33 - Prealgebra

Question

A concert ticket costs \(t\) dollars, a hamburger costs \(h\) dollars, and soda costs s dollars. Write an expression that represents the total cost of a ticket, hamburger, and soda for \(n\) people. (Lesson \(3-1\) )

Step-by-Step Solution

Answer

The total cost expression for \(n\) people is \( n(t + h + s) \).

Step 1: Define the Cost for One Person

First, we identify the costs involved for one person: a ticket costs \(t\) dollars, a hamburger costs \(h\) dollars, and soda costs \(s\) dollars. To find the total cost for one person, we sum these costs: \(t + h + s\).

Step 2: Multiply the Cost by Number of People

Next, to find the total cost for \(n\) people, we multiply the total cost for one person by \(n\). Thus, the expression is \( n(t + h + s) \).

Key Concepts

Cost Calculation

Cost calculation is an essential part of managing expenses, whether it's for a grocery list or planning an event. In this context, we're determining the total cost of a concert outing for multiple people. To do this, we need to:

• Identify all items you're paying for - here, it's a concert ticket, hamburger, and soda.
• Understand the individual cost of each item.
• Combine these costs to get the expense per person.
• Multiply by the number of people attending to find the total cost.

This process helps ensure accuracy in budgeting and avoids unexpected expenses.

Algebraic Expressions

Algebraic expressions are mathematical statements that use letters and symbols to represent numbers and quantities. They're crucial for solving problems where numerical values are not directly provided. In the exercise, we use variables and constants to express costs:

• Variables: The letters \(t\), \(h\), and \(s\) represent the cost of a ticket, hamburger, and soda respectively. \(n\) represents the number of people.
• Arithmetic Operators: We're using addition and multiplication to combine and scale these variables.

Thus, the expression \(n(t + h + s)\) is a compact representation of the cost for multiple people attending the concert. This algebraic expression can be easily adapted by inserting real numbers to solve specific problems.

Prealgebra

Prealgebra is a foundational math course that introduces students to basic algebraic concepts. It lays the groundwork needed for higher-level math courses. This topic prepares students by teaching key skills such as:

• Understanding and using variables instead of fixed numbers.
• Applying basic arithmetic operations to solve problems with variables.
• Setting up mathematical expressions to represent real-life scenarios, like cost calculations.

With prealgebra, students start handling mathematical symbols and developing logical problem-solving skills, just like in our original exercise involving cost calculations.