Equation For '5 Less Than N Is 28' Explained

Hey guys! Let's break down this math problem and figure out the right equation. It's all about translating words into mathematical expressions. We need to find the equation that correctly represents the statement: "Five less than a number ($n$) is 28."

Understanding the Problem

When we say "five less than a number," we're talking about subtracting 5 from that number. The number is represented by the variable $n$. So, "five less than $n$" can be written as $n - 5$. The problem tells us that this expression is equal to 28. Therefore, we need to find the equation that shows $n - 5$ equals 28.

Why not the other options? Let's look at why the other options aren't correct:

• A. $5 < 28n$: This inequality means "5 is less than 28 times $n$". This doesn't represent the problem statement at all. It involves multiplication and an inequality, neither of which are in the original problem.
• B. $5 - n = 28$: This equation means "5 minus $n$ equals 28." This is the opposite of what we need. We want 5 subtracted from $n$, not the other way around. This would imply that 5 is being reduced by some amount n to get to 28, which isn't what the original statement describes.
• D. $n - 28 = 5$: This equation means "$n$ minus 28 equals 5." This implies that we're starting with n, taking away 28, and ending up with 5. This is not the same as saying that 5 less than n is 28. It describes a different mathematical relationship. To illustrate, if we solved this equation, we'd find n = 33. Plugging that back into the original statement, "five less than 33 is 28," which is true. However, the equation itself doesn't directly translate the original problem statement.

Therefore, by carefully dissecting each option and comparing it to the original statement, we can confidently say that only one option accurately captures the relationship described.

The Correct Equation

The equation that correctly represents "five less than a number ($n$) is 28" is:

C. $n - 5 = 28$

This equation states that when you subtract 5 from the number $n$, the result is 28. This perfectly matches the original problem statement.

Therefore, the answer is C.

Why is Understanding the Translation Important?

Understanding how to translate word problems into mathematical equations is crucial in algebra and beyond. It's a foundational skill that allows you to solve a wide range of problems in various fields, including science, engineering, and finance.

• Problem-Solving: The ability to translate words into equations enables you to break down complex problems into smaller, manageable parts.
• Critical Thinking: This process encourages critical thinking as you analyze the relationships between different quantities.
• Real-World Applications: Many real-world scenarios can be modeled using mathematical equations. Being able to create these equations allows you to analyze and solve practical problems.

Strategies for Translating Word Problems

Here are some strategies to help you translate word problems into mathematical equations:

1. Read Carefully: Read the problem carefully and identify the key information. What are you trying to find? What information is given?
2. Define Variables: Assign variables to the unknown quantities. In our example, we used $n$ to represent the unknown number.
3. Identify Key Words: Look for key words that indicate mathematical operations. For example:
   • "Less than" means subtraction.
   • "More than" means addition.
   • "Times" means multiplication.
   • "Divided by" means division.
   • "Is" or "equals" means equals (=).
4. Write the Equation: Use the variables and key words to write the equation.
5. Check Your Answer: After solving the equation, check your answer to make sure it makes sense in the context of the problem.

Examples of Translating Phrases

Let's look at some more examples of translating phrases into mathematical expressions:

• "The sum of a number and 10" translates to $x + 10$ (where $x$ is the number).
• "Twice a number" translates to $2x$.
• "A number divided by 3" translates to $x / 3$ or $\frac{x}{3}$.
• "7 more than twice a number" translates to $2x + 7$.

Practice Problems

To solidify your understanding, try these practice problems:

1. Nine more than a number is 34. Write the equation.
2. Six less than twice a number is 18. Write the equation.
3. A number divided by 4 is 7. Write the equation.

Conclusion

Translating word problems into mathematical equations is a fundamental skill in mathematics. By carefully reading the problem, defining variables, identifying key words, and writing the equation, you can successfully solve a wide range of problems. Remember to always check your answer to ensure it makes sense in the context of the problem. So next time you see a word problem, don't panic! Break it down, translate it step by step, and you'll be solving equations like a pro in no time! Keep practicing, and you'll get the hang of it, guys! This is a skill that really pays off in the long run. Whether you're calculating your budget, figuring out cooking measurements, or tackling complex scientific problems, the ability to translate words into math is essential. So keep at it, and remember to have fun with it! You got this! Remember, the key is to practice, practice, practice. The more you work at it, the easier it will become. And don't be afraid to ask for help when you need it. There are plenty of resources available to help you succeed in math. Good luck, and happy solving! Let's keep learning and growing together. Math can be an adventure, so embrace the challenge and see where it takes you! You might be surprised at what you can achieve. Keep up the great work!