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Chapter 2: Problem 59

Monica is \(x\) years old. What expression represents her age 15 yr from now? 5 yr ago?

Short Answer

Expert verified
15 years from now: \( x + 15 \). 5 years ago: \( x - 5 \).

Step by step solution

01

- Define the Current Age

Let Monica's current age be represented by the variable, which is given as \( x \).
02

- Calculate Age 15 Years from Now

To find Monica's age 15 years from now, add 15 to her current age \( x \). This can be represented by the expression: \( x + 15 \).
03

- Calculate Age 5 Years Ago

To find Monica's age 5 years ago, subtract 5 from her current age \( x \). This can be represented by the expression: \( x - 5 \).

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

current age
Understanding the 'current age' concept is essential in solving age-related algebra problems. In these problems, we often start by defining the current age of a person using a variable. Here, we define Monica's current age as \(x\). This means that wherever we see the variable \(x\) in our expressions, it represents Monica's current age.
  • Using variables simplifies the calculations and relationships with other ages.
  • In our case, \(x\) is Monica's current age.
All further calculations and expressions for future or past ages are determined based on Monica's current age, represented by \(x\).
age calculation
Age calculation is a fundamental part of algebra problems involving time. These calculations can address both future and past ages:
  • **Future Age Calculation**: To determine Monica鈥檚 age 15 years from now, we add 15 years to her current age \(x\). This is because we always add future time to the current age. Therefore, Monica's age in 15 years is represented by the expression \(x + 15\).
  • **Past Age Calculation**: To determine Monica鈥檚 age 5 years ago, we subtract 5 years from her current age \(x\). This is because we always subtract past time from the current age. Thus, Monica鈥檚 age 5 years ago is represented by the expression \(x - 5\).
These calculations help us understand how Monica's age changes over time, using simple arithmetic operations on the variable representing her current age.
variable representation
Variable representation is a key algebraic concept where letters or symbols are used to stand for numbers. In this exercise, the variable \(x\) stands for Monica's current age.
  • Variables make it easier to write general expressions and solve problems logically.
  • They help to convey relationships between different quantities effectively.
When we represent Monica鈥檚 future age as \(x + 15\) or past age as \(x - 5\), we are using the strength of variable representation. This approach helps in formulating and solving equations systematically.

By understanding and applying the concept of variables, students can solve a wide range of problems with varying complexities simply and effectively.

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