Translate This Sentence Into An Equation: 48 Is The Product Of 3 And Carlos's Score. Use The Variable { C $}$ To Represent Carlos's Score. Equation: { 48 = 3c $}$

Introduction

Mathematics is a language that uses numbers, symbols, and equations to describe the world around us. In this article, we will explore how to translate verbal descriptions into mathematical equations. We will use a simple sentence as an example to demonstrate the process.

The Sentence

The sentence we will use is: "48 is the product of 3 and Carlos's score." This sentence can be translated into a mathematical equation using the variable $c$ to represent Carlos's score.

Translating the Sentence

To translate the sentence into a mathematical equation, we need to identify the key elements:

• The product of 3 and Carlos's score: This means that we need to multiply 3 by Carlos's score.
• The result of the product is 48: This means that the result of multiplying 3 by Carlos's score is equal to 48.

Using the variable $c$ to represent Carlos's score, we can write the equation as:

$$48 = 3c$$

Understanding the Equation

The equation $48 = 3c$ tells us that the result of multiplying 3 by Carlos's score is equal to 48. To solve for Carlos's score, we need to isolate the variable $c$.

Solving for Carlos's Score

To solve for Carlos's score, we can divide both sides of the equation by 3:

$$\frac{48}{3} = c$$

$$16 = c$$

Therefore, Carlos's score is 16.

Discussion

Translating verbal descriptions into mathematical equations is an important skill in mathematics. It allows us to describe complex situations using simple equations and to solve problems using mathematical techniques.

Real-World Applications

Translating verbal descriptions into mathematical equations has many real-world applications. For example:

• In business, mathematical equations can be used to model sales, profits, and losses.
• In science, mathematical equations can be used to model physical systems, such as the motion of objects or the behavior of populations.
• In engineering, mathematical equations can be used to design and optimize systems, such as bridges or electronic circuits.

Conclusion

In this article, we have seen how to translate a verbal description into a mathematical equation. We have used a simple sentence as an example and have demonstrated how to solve for the variable $c$. Translating verbal descriptions into mathematical equations is an important skill in mathematics and has many real-world applications.

Additional Examples

Here are a few more examples of translating verbal descriptions into mathematical equations:

• "The sum of 2 and 5 is 7." This can be translated into the equation $2 + 5 = 7$.
• "The difference between 10 and 3 is 7." This can be translated into the equation $10 - 3 = 7$.
• "The product of 4 and 6 is 24." This can be translated into the equation $4 \times 6 = 24$.

Practice Problems

Here are a few practice problems to help you practice translating verbal descriptions into mathematical equations:

• "The sum of 3 and 2 is 5."
• "The difference between 8 and 2 is 6."
• "The product of 5 and 3 is 15."

Answer Key

Here are the answers to the practice problems:

• $3 + 2 = 5$
• $8 - 2 = 6$
• $5 \times 3 = 15$

Conclusion

Q: What is the purpose of translating verbal descriptions into mathematical equations?

A: The purpose of translating verbal descriptions into mathematical equations is to describe complex situations using simple equations and to solve problems using mathematical techniques.

Q: How do I know when to use addition, subtraction, multiplication, or division in a mathematical equation?

A: To determine which operation to use in a mathematical equation, you need to read the verbal description carefully and identify the key elements. For example, if the verbal description says "the sum of 2 and 5 is 7", you would use addition to write the equation as $2 + 5 = 7$.

Q: What is the difference between a variable and a constant in a mathematical equation?

A: A variable is a letter or symbol that represents a value that can change, while a constant is a value that does not change. In the equation $48 = 3c$, $c$ is a variable because it represents Carlos's score, which can change. The number 48 is a constant because it is a fixed value.

Q: How do I solve for a variable in a mathematical equation?

A: To solve for a variable in a mathematical equation, you need to isolate the variable by performing the opposite operation to the one that is being performed on it. For example, in the equation $48 = 3c$, you can solve for $c$ by dividing both sides of the equation by 3: $\frac{48}{3} = c$.

Q: What is the order of operations in a mathematical equation?

A: The order of operations in a mathematical equation 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: Can I use mathematical equations to solve real-world problems?

A: Yes, mathematical equations can be used to solve real-world problems. For example, in business, mathematical equations can be used to model sales, profits, and losses. In science, mathematical equations can be used to model physical systems, such as the motion of objects or the behavior of populations.

Q: What are some common mistakes to avoid when translating verbal descriptions into mathematical equations?

A: Some common mistakes to avoid when translating verbal descriptions into mathematical equations include:

• Not reading the verbal description carefully and missing important details.
• Using the wrong operation (e.g. using addition instead of subtraction).
• Not isolating the variable correctly.
• Not checking the equation for errors.

Q: How can I practice translating verbal descriptions into mathematical equations?

A: You can practice translating verbal descriptions into mathematical equations by:

• Reading and writing mathematical equations regularly.
• Solving practice problems and exercises.
• Working with a tutor or teacher to review and practice.
• Using online resources and tools to practice and learn.

Conclusion

Translating verbal descriptions into mathematical equations is an important skill in mathematics. By understanding the purpose and process of translating verbal descriptions into mathematical equations, you can become proficient in solving problems using mathematical techniques. With practice and patience, you can master this skill and apply it to a wide range of real-world problems.