Sam Is 10 Years Younger Than One-half The Age Of His Aunt. Let \[$ A \$\] Represent His Aunt's Age. Which Algebraic Expression Can Be Used To Determine Sam's Age If His Aunt Is 40?A. \[$\frac{a}{10} - 2\$\]; When \[$ A = 40
Introduction
Algebraic expressions are a fundamental concept in mathematics, used to represent and solve various mathematical problems. In this article, we will explore how to determine Sam's age using an algebraic expression, given that his aunt is 40 years old. We will use the information provided to create an algebraic expression that can be used to find Sam's age.
Understanding the Problem
Sam is 10 years younger than one-half the age of his aunt. Let { a $}$ represent his aunt's age. We need to find an algebraic expression that can be used to determine Sam's age if his aunt is 40.
Step 1: Define the Algebraic Expression
To determine Sam's age, we need to create an algebraic expression that represents the relationship between Sam's age and his aunt's age. Let's start by defining the expression.
Sam's age is 10 years younger than one-half the age of his aunt. This can be represented as:
{ \frac{a}{2} - 10 $}$
This expression represents the relationship between Sam's age and his aunt's age.
Step 2: Substitute the Value of a
Now that we have the algebraic expression, we need to substitute the value of { a $}$ with 40, since we are given that his aunt is 40 years old.
{ \frac{a}{2} - 10 $}$
Substituting { a = 40 $}$:
{ \frac{40}{2} - 10 $}$
Simplifying the expression:
{ 20 - 10 $}$
{ 10 $}$
Therefore, the algebraic expression that can be used to determine Sam's age if his aunt is 40 is:
{ \frac{a}{2} - 10 $}$
Conclusion
In this article, we have explored how to determine Sam's age using an algebraic expression, given that his aunt is 40 years old. We have created an algebraic expression that represents the relationship between Sam's age and his aunt's age, and then substituted the value of { a $}$ with 40 to find Sam's age.
Final Answer
The final answer is:
Discussion
This problem is a great example of how algebraic expressions can be used to solve real-world problems. By understanding the relationship between Sam's age and his aunt's age, we can create an algebraic expression that can be used to determine Sam's age.
Related Problems
- If Sam is 10 years younger than one-half the age of his aunt, and his aunt is 50 years old, what is Sam's age?
- If Sam is 10 years younger than one-half the age of his aunt, and his aunt is 60 years old, what is Sam's age?
Solutions
-
If Sam is 10 years younger than one-half the age of his aunt, and his aunt is 50 years old, what is Sam's age?
{ \frac{a}{2} - 10 $}$
Substituting { a = 50 $}$:
{ \frac{50}{2} - 10 $}$
Simplifying the expression:
{ 25 - 10 $}$
{ 15 $}$
Therefore, Sam's age is 15.
-
If Sam is 10 years younger than one-half the age of his aunt, and his aunt is 60 years old, what is Sam's age?
{ \frac{a}{2} - 10 $}$
Substituting { a = 60 $}$:
{ \frac{60}{2} - 10 $}$
Simplifying the expression:
{ 30 - 10 $}$
{ 20 $}$
Therefore, Sam's age is 20.
Solving Algebraic Expressions: Determining Sam's Age =====================================================
Q&A: Determining Sam's Age
Q: What is the algebraic expression that can be used to determine Sam's age if his aunt is 40?
A: The algebraic expression that can be used to determine Sam's age if his aunt is 40 is:
{ \frac{a}{2} - 10 $}$
Q: How do I substitute the value of a in the algebraic expression?
A: To substitute the value of { a $}$ in the algebraic expression, simply replace { a $}$ with the given value. For example, if his aunt is 40 years old, we substitute { a = 40 $}$ in the expression:
{ \frac{a}{2} - 10 $}$
{ \frac{40}{2} - 10 $}$
Simplifying the expression:
{ 20 - 10 $}$
{ 10 $}$
Q: What is the final answer if his aunt is 40 years old?
A: The final answer is:
Q: If Sam is 10 years younger than one-half the age of his aunt, and his aunt is 50 years old, what is Sam's age?
A: To find Sam's age, we substitute { a = 50 $}$ in the expression:
{ \frac{a}{2} - 10 $}$
{ \frac{50}{2} - 10 $}$
Simplifying the expression:
{ 25 - 10 $}$
{ 15 $}$
Therefore, Sam's age is 15.
Q: If Sam is 10 years younger than one-half the age of his aunt, and his aunt is 60 years old, what is Sam's age?
A: To find Sam's age, we substitute { a = 60 $}$ in the expression:
{ \frac{a}{2} - 10 $}$
{ \frac{60}{2} - 10 $}$
Simplifying the expression:
{ 30 - 10 $}$
{ 20 $}$
Therefore, Sam's age is 20.
Q: What is the relationship between Sam's age and his aunt's age?
A: The relationship between Sam's age and his aunt's age is that Sam is 10 years younger than one-half the age of his aunt.
Q: How can I use this algebraic expression to solve other problems?
A: This algebraic expression can be used to solve other problems where Sam's age is related to his aunt's age. Simply substitute the value of { a $}$ with the given value and solve for Sam's age.
Conclusion
In this article, we have explored how to determine Sam's age using an algebraic expression, given that his aunt is 40 years old. We have created an algebraic expression that represents the relationship between Sam's age and his aunt's age, and then substituted the value of { a $}$ with 40 to find Sam's age. We have also answered several questions related to this problem, including how to substitute the value of { a $}$, what the final answer is if his aunt is 40 years old, and how to use this algebraic expression to solve other problems.