Breaking Down the Statement

Oct 13, 2025 by leolavanderia.com.br 65 views

Which Equation is a Translation of "Three Times P Plus Twenty-One is Forty-Two"?

Understanding the Problem

When we are given a mathematical statement, such as "three times p plus twenty-one is forty-two," we need to translate it into an equation. This involves rewriting the statement in a way that uses mathematical symbols and operations to represent the relationship between the variables and constants.

Breaking Down the Statement

Let's break down the given statement into its individual components:

"Three times p" can be represented as 3p, where p is the variable.
"Plus twenty-one" means we need to add 21 to the previous expression, resulting in 3p + 21.
"Is forty-two" indicates that the resulting expression is equal to 42.

Translating the Statement into an Equation

Now that we have broken down the statement, we can translate it into an equation. The equation should have the following form:

3p + 21 = 42

This equation represents the relationship between the variable p and the constant 42, with the additional constant 21 being added to the product of 3 and p.

Evaluating the Answer Choices

Let's evaluate the answer choices to determine which one represents the correct translation of the given statement.

A) $p + 21 \cdot 3 = 42$

This equation is incorrect because it does not represent the correct translation of the statement. The expression "three times p" is represented as p, not 3p.

B) $3(21) + p = 42$

This equation is also incorrect because it does not represent the correct translation of the statement. The expression "three times p" is represented as p, not 3p, and the expression "plus twenty-one" is represented as adding 21 to the product of 3 and 21, not to 3p.

C) $3p + 21 = 42$

This equation is correct because it represents the correct translation of the given statement. The expression "three times p" is represented as 3p, and the expression "plus twenty-one" is represented as adding 21 to 3p.

D) $21 + \frac{3}{p} = 42$

This equation is incorrect because it does not represent the correct translation of the statement. The expression "three times p" is represented as the fraction 3/p, not 3p.

Conclusion

Based on our analysis, the correct answer is C) $3p + 21 = 42$ . This equation represents the correct translation of the given statement, with the expression "three times p" being represented as 3p and the expression "plus twenty-one" being represented as adding 21 to 3p.

Understanding Translations in Mathematics

Translations in mathematics involve rewriting a statement or expression in a different form, often using different mathematical symbols or operations. In the context of the given problem, we need to translate the statement "three times p plus twenty-one is forty-two" into an equation.

Key Concepts

Translations in mathematics involve rewriting a statement or expression in a different form.
The expression "three times p" can be represented as 3p.
The expression "plus twenty-one" means we need to add 21 to the previous expression.
The resulting expression is equal to 42.

Real-World Applications

Translations in mathematics have many real-world applications, including:

Algebra: Translations are used to rewrite algebraic expressions in a different form, often to simplify or solve equations.
Geometry: Translations are used to describe the movement of objects in space, such as translating a shape from one position to another.
Data Analysis: Translations are used to rewrite data in a different form, often to make it easier to analyze or visualize.

Common Mistakes

When translating a statement into an equation, it's common to make mistakes such as:

Misrepresenting the expression "three times p" as p, not 3p.
Misrepresenting the expression "plus twenty-one" as adding 21 to the product of 3 and 21, not to 3p.
Misrepresenting the expression "is forty-two" as an inequality, not an equation.

Conclusion

In conclusion, the correct answer is C) $3p + 21 = 42$ . This equation represents the correct translation of the given statement, with the expression "three times p" being represented as 3p and the expression "plus twenty-one" being represented as adding 21 to 3p.
Q&A: Translations in Mathematics

Frequently Asked Questions

Q: What is a translation in mathematics?

A: A translation in mathematics is the process of rewriting a statement or expression in a different form, often using different mathematical symbols or operations.

Q: How do I translate a statement into an equation?

A: To translate a statement into an equation, you need to break down the statement into its individual components and represent each component using mathematical symbols and operations. For example, if the statement is "three times p plus twenty-one is forty-two," you would represent "three times p" as 3p, "plus twenty-one" as adding 21 to 3p, and "is forty-two" as an equation equal to 42.

Q: What are some common mistakes to avoid when translating a statement into an equation?

A: Some common mistakes to avoid when translating a statement into an equation include:

Misrepresenting the expression "three times p" as p, not 3p.
Misrepresenting the expression "plus twenty-one" as adding 21 to the product of 3 and 21, not to 3p.
Misrepresenting the expression "is forty-two" as an inequality, not an equation.

Q: How do I know if I have translated a statement correctly into an equation?

A: To determine if you have translated a statement correctly into an equation, you need to check that each component of the statement is represented correctly using mathematical symbols and operations. You should also check that the resulting equation is consistent with the original statement.

Q: What are some real-world applications of translations in mathematics?

A: Translations in mathematics have many real-world applications, including:

Algebra: Translations are used to rewrite algebraic expressions in a different form, often to simplify or solve equations.
Geometry: Translations are used to describe the movement of objects in space, such as translating a shape from one position to another.
Data Analysis: Translations are used to rewrite data in a different form, often to make it easier to analyze or visualize.

Q: Can you provide an example of a translation in mathematics?

A: Yes, here is an example of a translation in mathematics:

Original statement: "Five times x minus three is twenty-one"

Translated equation: 5x - 3 = 21

In this example, the original statement is translated into an equation by representing "five times x" as 5x, "minus three" as subtracting 3 from 5x, and "is twenty-one" as an equation equal to 21.

Q: How do I practice translating statements into equations?

A: To practice translating statements into equations, you can try the following:

Start with simple statements and gradually move on to more complex ones.
Use online resources or math textbooks to find examples of translations in mathematics.
Practice translating statements into equations regularly to build your skills and confidence.

Q: What are some tips for translating statements into equations?

A: Some tips for translating statements into equations include:

Read the statement carefully and break it down into its individual components.
Represent each component using mathematical symbols and operations.
Check that the resulting equation is consistent with the original statement.
Practice regularly to build your skills and confidence.

Conclusion

In conclusion, translations in mathematics are an important concept that involves rewriting a statement or expression in a different form, often using different mathematical symbols or operations. By understanding how to translate statements into equations, you can improve your math skills and build your confidence in solving problems.