Problem 11 - Beginning and Intermediate Algebra

Question

The spring 2007 tuition and fees for a Texas resident undergraduate student at University of Texas at El Paso were approximately \(\$ 2631\) for a 15 -credit load. At the same time the tuition and fees for a Florida resident attending University of Florida were approximately \(\$ 2456 .\) Write an inequality state. ment using \(<\) or \(>\) comparing the numbers 2631 and 2456.

Step-by-Step Solution

Answer

The inequality is \( 2631 > 2456 \).

Step 1: Understand the Problem

We are given two amounts: $2631 for a Texas resident undergraduate student and $2456 for a Florida resident. We need to compare these two numbers using the symbols '<' or '>'. This will help us to state which amount is greater.

Step 2: Set Up the Comparison

We will write the inequality statement to represent the relationship. Since $2631 is the tuition fee for Texas residents and $2456 for Florida residents, we want to determine if $2631 is greater or less than $2456.

Step 3: Compare the Amounts

To compare the amounts, observe if $2631 is greater than or less than $2456. Clearly, $2631 is greater than $2456.

Step 4: Write the Inequality

Based on our comparison in the previous step, we establish that \(2631 > \)2456. Therefore, the inequality statement is as follows: \[ 2631 > 2456 \]

Key Concepts

Tuition Comparison

When considering tuition comparison, students often look at the cost of attending different universities. In this example, we examine the tuition and fees for a 15-credit load at two universities: the University of Texas at El Paso and the University of Florida. For Texas residents, the tuition is \(\\(2631\), while Florida residents face a tuition of \(\\)2456\).
By comparing these numbers, one can determine which university has the higher tuition fees. Understanding this comparison helps students make informed decisions about their education expenses.

• University of Texas at El Paso: \(\\(2631\)
• University of Florida: \(\\)2456\)

This comparison emphasizes the importance of evaluating tuition costs across various institutions, allowing students to budget effectively for their education.

Number Comparison

Number comparison is a fundamental mathematical skill, often used when we need to determine which of two numbers is larger or smaller. In real-world scenarios, this can involve comparing prices, measurements, or other numerical data. For this exercise, we are asked to compare two amounts: \(2631\) and \(2456\).
To compare numbers:

• Align the digits based on their positions, usually starting from the leftmost digit.
• If the leftmost digits are different, the comparison is straightforward as the number with the higher digit in the highest place value is greater.
• If digits are the same, proceed to the next digit to the right until you find a difference.

In our example, \(2631\) has a larger digit in the thousands place compared to \(2456\), making it clear that \(2631 > 2456\). This comparison enables us to comprehend the numerical relationship between the two figures.

Inequality Symbols

Inequality symbols are vital in mathematics, allowing us to compare numbers and understand their relationships. These symbols include:

• \(<\): Represents "less than." Used when the first number is smaller than the second.
• \(>\): Represents "greater than." Applied when the first number is larger than the second.
• \(\leq\) and \(\geq\): Represent "less than or equal to" and "greater than or equal to," respectively.

In our exercise, the tuition fees of \(2631\) for Texas and \(2456\) for Florida need to be compared. By observing, we realize \(2631 > 2456\). Therefore, the appropriate symbol in this case is the greater-than symbol \(>\).
Recognizing and correctly using inequality symbols is essential for creating accurate mathematical statements that describe the size relationship between two or more numbers.