Problem 73 - Elementary and Intermediate Algebra

Question

Answer with an algebraic expression. See Example 9. A ticket to a concert costs \(\$ t .\) What would a pair of concert tickets cost?

Step-by-Step Solution

Answer

The cost of a pair of tickets is \(2t\).

Step 1: Understanding the Problem

To find the cost of a pair of concert tickets, we need to calculate the total cost for two tickets, each priced at \( \$ t \). This involves simple multiplication.

Step 2: Setting Up the Expression

Since a pair means two tickets, we need to multiply the price of one ticket \( t \) by 2. This gives us an algebraic expression for the total cost.

Step 3: Writing the Expression

The expression for the cost of a pair of tickets is \( 2t \). This represents twice the cost of one ticket.

Key Concepts

multiplication in algebra

Multiplication in algebra is crucial because it allows us to calculate unknown quantities. In algebra, instead of using numbers alone, we often deal with variables, which are symbols like \(t\) that stand in for unknown values. Imagine the variable \(t\) represents the cost of a single concert ticket.To find how much two tickets cost, you need to multiply this single ticket cost \(t\) by 2. This multiplication is expressed as \(2t\), where the number 2 is the coefficient, and \(t\) is the variable.

• The coefficient tells us how many times to count the variable, indicating scaling.
• This simple multiplication translates to doubling the original value.

Understanding multiplication in this context opens doors to tackling more complex algebraic problems, where one equation might have several variables and coefficients.

understanding algebra problems

Understanding algebra problems is like cracking a code. The problem's language must be translated into mathematical expressions. Start by parsing the given information. Make sure to note what each variable represents. In our example, \(t\) represents the price of one concert ticket.Breaking down the problem into smaller, manageable steps can greatly help. First, identify what you're solving for. Next, determine what operations are necessary to reach that solution. In this scenario, we need to find the total cost for two tickets.

• Recognize keywords like 'pair', indicating two items are involved.
• Use the provided variable to form your mathematical expression using known operations.

By practicing these steps, you improve your ability to decode and solve various algebra problems efficiently.

writing algebraic expressions

Writing algebraic expressions involves converting a real-life problem into a mathematical form. It's all about representing relationships between variables and numbers in a compact and precise way. Take the concert ticket cost example:Firstly, identify what needs to be expressed. Here, the task is to find the cost for two tickets. Hence, we start with the known variable \(t\), representing the single ticket price.Then, determine what operations to use. Since we're dealing with a pair of tickets, we'll use multiplication to find the cost for two, leading us to the expression \(2t\).

• Ensure clarity—each part of the expression should relate directly to the problem.
• Keep it simple—avoid adding irrelevant elements that could complicate the expression.

With consistent practice in writing algebraic expressions, developing a knack for it can lead to mastery. This skill is pivotal in progressing within algebra and solving increasingly challenging problems.