Problem 79 - Intermediate Algebra

Question

Answer the question with an algebraic expression. Brian is \(n\) years old. How old will he be in 20 years?

Step-by-Step Solution

Answer

Brian will be \(n + 20\) years old.

Step 1: Understanding the Problem

The problem asks how old Brian will be in 20 years. We know that his current age is represented by the variable \(n\).

Step 2: Setting Up the Expression

To find Brian's age in 20 years, we need to add 20 to his current age. This can be expressed as \(n + 20\).

Step 3: Conclusion

The algebraic expression representing Brian's age in 20 years is \(n + 20\).

Key Concepts

Age Problems

Age problems are a common type of mathematical challenge that involve determining ages at different times, either in the future or past. These problems often require us to comprehend the relationship between present and future or past ages in a logical manner. They serve as excellent exercises to apply algebraic concepts practically.

• In these problems, we're usually given the current age of a person or object.
• The task often is to calculate the age at another time by adding or subtracting years.
• Age problems help us practice setting up equations correctly and interpreting results in a real-life context.

Age problems, like the one in the exercise, help bridge theoretical math with everyday scenarios, making math more relatable and interesting.

Basic Algebra

Basic algebra is the foundation of understanding how to work with variables and equations. Key to solving problems like age problems is knowing how to manipulate and solve expressions step-by-step. Algebra enables us to represent unknown quantities as variables and create equations that describe relationships between known and unknown values.

• It involves working with symbols and letters to represent numbers.
• Addition and subtraction are often used in forming expressions - both are evident in daily calculations and more complex mathematical problems.
• Algebra lays the groundwork for more advanced topics in math, including geometry and calculus.

Mastering basic algebra allows one to solve real-world problems, understand patterns, and use reasoning effectively.

Variable Representation

Variable representation is crucial in algebra as it allows us to generalize and solve a wide array of problems. A variable is typically denoted by a letter, like 'n' in the age problem, representing an unknown quantity that can change. This concept is useful because:

• It simplifies complex problems by substituting known values with letters.
• Variables enable us to build equations that are easily manipulable to find desired results.
• They can represent anything from ages, distances, or even costs, making equations adaptable to various scenarios.

Understanding how to effectively use variables is paramount in both creating and solving algebraic expressions. By using variables, we bring a sense of uniformity and simplification to complex mathematical problems.