14) Juan's Age Is 4 Years Less Than Two Times Pedro's Age. Which Expression Represents Juan's Age?A) $4a + 2$ B) $2a + 4$ C) $2a - 4$ D) $4a - 2$ 15) If Pedro Is 16 Years Old, How Old Is Juan?A) 32 B) 28 C) 12

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Introduction

In algebra, understanding relationships between variables is crucial for solving equations and making predictions. In this article, we will explore a scenario where Juan's age is related to Pedro's age, and we will use algebraic expressions to represent this relationship. We will also use a specific value for Pedro's age to determine Juan's age.

Juan's Age in Terms of Pedro's Age

Let's assume Pedro's age is represented by the variable "a". We are given that Juan's age is 4 years less than two times Pedro's age. To represent this relationship algebraically, we need to translate the given information into an expression.

  • Two times Pedro's age is represented by 2a.
  • Four years less than two times Pedro's age is represented by 2a - 4.

Therefore, the expression that represents Juan's age is 2a - 4.

Option Analysis

Let's analyze the given options to see which one matches our expression:

  • Option A: 4a + 2
  • Option B: 2a + 4
  • Option C: 2a - 4
  • Option D: 4a - 2

Only option C matches our expression, which is 2a - 4.

Pedro's Age and Juan's Age

Now that we have the expression for Juan's age, let's use a specific value for Pedro's age to determine Juan's age. We are given that Pedro is 16 years old. To find Juan's age, we substitute a = 16 into the expression 2a - 4.

Calculating Juan's Age

Substituting a = 16 into the expression 2a - 4, we get:

2(16) - 4 = 32 - 4 = 28

Therefore, if Pedro is 16 years old, Juan is 28 years old.

Conclusion

In this article, we used algebraic expressions to represent the relationship between Juan's age and Pedro's age. We determined that the expression 2a - 4 represents Juan's age and used a specific value for Pedro's age to find Juan's age. By understanding these relationships, we can make predictions and solve equations in algebra.

Key Takeaways

  • Algebraic expressions can be used to represent relationships between variables.
  • The expression 2a - 4 represents Juan's age in terms of Pedro's age.
  • By substituting a specific value for Pedro's age into the expression, we can determine Juan's age.

Practice Problems

  1. If Juan's age is 4 years less than two times Pedro's age, and Pedro is 20 years old, how old is Juan?
  2. If Juan's age is 2 years more than three times Pedro's age, and Pedro is 15 years old, how old is Juan?

Answer Key

  1. 36
  2. 51
    Algebraic Relationships: Q&A =============================

Introduction

In our previous article, we explored the relationship between Juan's age and Pedro's age using algebraic expressions. We determined that the expression 2a - 4 represents Juan's age in terms of Pedro's age. In this article, we will answer some frequently asked questions related to algebraic relationships.

Q&A

Q: What is an algebraic expression?

A: An algebraic expression is a combination of variables, constants, and mathematical operations that can be evaluated to produce a value.

Q: How do I represent a relationship between two variables using an algebraic expression?

A: To represent a relationship between two variables using an algebraic expression, you need to identify the variables and the relationship between them. For example, if Juan's age is 4 years less than two times Pedro's age, you can represent this relationship using the expression 2a - 4.

Q: What is the difference between a variable and a constant in an algebraic expression?

A: A variable is a symbol that represents a value that can change, while a constant is a value that remains the same. In the expression 2a - 4, "a" is a variable and 4 is a constant.

Q: How do I evaluate an algebraic expression?

A: To evaluate an algebraic expression, you need to substitute the values of the variables into the expression and perform the mathematical operations. For example, if we substitute a = 16 into the expression 2a - 4, we get 2(16) - 4 = 32 - 4 = 28.

Q: What is the order of operations in algebraic expressions?

A: The order of operations in algebraic expressions is:

  1. Parentheses: Evaluate expressions inside parentheses first.
  2. Exponents: Evaluate any exponential expressions next.
  3. Multiplication and Division: Evaluate any multiplication and division operations from left to right.
  4. Addition and Subtraction: Finally, evaluate any addition and subtraction operations from left to right.

Q: How do I simplify an algebraic expression?

A: To simplify an algebraic expression, you need to combine like terms and eliminate any unnecessary operations. For example, the expression 2a + 4a can be simplified to 6a by combining the like terms.

Q: What is the difference between an equation and an expression in algebra?

A: An equation is a statement that says two expressions are equal, while an expression is a combination of variables, constants, and mathematical operations that can be evaluated to produce a value.

Q: How do I solve an equation in algebra?

A: To solve an equation in algebra, you need to isolate the variable on one side of the equation. This can be done by adding, subtracting, multiplying, or dividing both sides of the equation by the same value.

Conclusion

In this article, we answered some frequently asked questions related to algebraic relationships. We covered topics such as algebraic expressions, variables and constants, evaluating expressions, order of operations, simplifying expressions, and solving equations. By understanding these concepts, you can become proficient in algebra and solve a wide range of problems.

Key Takeaways

  • Algebraic expressions can be used to represent relationships between variables.
  • Variables and constants are used in algebraic expressions to represent values that can change and remain the same.
  • Evaluating algebraic expressions involves substituting values into the expression and performing mathematical operations.
  • Simplifying algebraic expressions involves combining like terms and eliminating unnecessary operations.
  • Solving equations in algebra involves isolating the variable on one side of the equation.

Practice Problems

  1. If Juan's age is 4 years less than two times Pedro's age, and Pedro is 20 years old, how old is Juan?
  2. If Juan's age is 2 years more than three times Pedro's age, and Pedro is 15 years old, how old is Juan?
  3. Simplify the expression 2a + 4a.
  4. Evaluate the expression 2(16) - 4.
  5. Solve the equation 2x + 5 = 11.

Answer Key

  1. 36
  2. 51
  3. 6a
  4. 28
  5. x = 3