Adding 17 to the Expression

Oct 13, 2025 by recoveryshake.com 62 views

In this article, we will delve into a mathematical problem that involves understanding fractions and algebraic expressions. The problem revolves around Barry's baseball card collection and his brother's collection. We will explore how to represent the number of baseball cards Barry has in terms of the number of cards his brother has.

The Problem Statement

Barry has 17 more than two-thirds of the number of cards in his brother's baseball card collection. If $x$ represents the number of baseball cards his brother has, we need to find an expression that represents the number of baseball cards Barry has.

Breaking Down the Problem

To solve this problem, we need to understand the concept of fractions and how to represent them algebraically. We are given that Barry has 17 more than two-thirds of the number of cards in his brother's collection. This means that we need to find two-thirds of the number of cards his brother has and then add 17 to it.

Representing Two-Thirds Algebraically

Two-thirds of a number can be represented algebraically as $\frac{2}{3}x$ , where $x$ is the number of cards his brother has. This is because we are multiplying the number of cards by $\frac{2}{3}$ to find two-thirds of the number.

Adding 17 to the Expression

Now that we have found two-thirds of the number of cards his brother has, we need to add 17 to it. This can be represented algebraically as $\frac{2}{3}x + 17$ . This expression represents the number of baseball cards Barry has in terms of the number of cards his brother has.

The Final Expression

Therefore, the expression that represents the number of baseball cards Barry has is $\frac{2}{3}x + 17$ .

Conclusion

In this article, we have explored a mathematical problem that involves understanding fractions and algebraic expressions. We have seen how to represent two-thirds of a number algebraically and how to add 17 to the expression to find the number of baseball cards Barry has. The final expression is $\frac{2}{3}x + 17$ , which represents the number of baseball cards Barry has in terms of the number of cards his brother has.

Key Takeaways

Two-thirds of a number can be represented algebraically as $\frac{2}{3}x$ .
Adding 17 to the expression $\frac{2}{3}x$ gives us the number of baseball cards Barry has.
The final expression that represents the number of baseball cards Barry has is $\frac{2}{3}x + 17$ .

Real-World Applications

This problem has real-world applications in various fields, such as finance, economics, and engineering. Understanding fractions and algebraic expressions is crucial in these fields, as it helps us to represent complex relationships and make informed decisions.

Future Directions

In the future, we can explore more complex mathematical problems that involve fractions and algebraic expressions. We can also apply these concepts to real-world problems and see how they can be used to make informed decisions.

References

[1] "Algebra and Trigonometry" by Michael Sullivan
[2] "Mathematics for Economists" by Carl P. Simon and Lawrence Blume

Glossary

Fraction: A way of representing a part of a whole as a ratio of two numbers.
Algebraic Expression: A mathematical expression that involves variables and constants.
Variable: A symbol that represents a value that can change.
Constant: A value that does not change.

FAQs

Q: What is the expression that represents the number of baseball cards Barry has? A: The expression that represents the number of baseball cards Barry has is $\frac{2}{3}x + 17$ .
Q: How do we represent two-thirds of a number algebraically? A: We represent two-thirds of a number algebraically as $\frac{2}{3}x$ .
Q: What is the final expression that represents the number of baseball cards Barry has? A: The final expression that represents the number of baseball cards Barry has is $\frac{2}{3}x + 17$ .
Q&A: Understanding the Problem and Its Solutions =====================================================

In this article, we will continue to explore the problem of Barry's baseball card collection and his brother's collection. We will answer some frequently asked questions (FAQs) related to the problem and provide additional insights into the solution.

Q: What is the problem statement?

A: The problem statement is as follows: Barry has 17 more than two-thirds of the number of cards in his brother's baseball card collection. If $x$ represents the number of baseball cards his brother has, we need to find an expression that represents the number of baseball cards Barry has.

Q: How do we represent two-thirds of a number algebraically?

A: We represent two-thirds of a number algebraically as $\frac{2}{3}x$ , where $x$ is the number of cards his brother has. This is because we are multiplying the number of cards by $\frac{2}{3}$ to find two-thirds of the number.

Q: What is the expression that represents the number of baseball cards Barry has?

A: The expression that represents the number of baseball cards Barry has is $\frac{2}{3}x + 17$ . This is because we are adding 17 to two-thirds of the number of cards his brother has.

Q: Why do we need to add 17 to the expression?

A: We need to add 17 to the expression because Barry has 17 more than two-thirds of the number of cards in his brother's collection. This means that we need to add 17 to two-thirds of the number of cards his brother has to find the number of baseball cards Barry has.

Q: Can we simplify the expression?

A: Yes, we can simplify the expression. However, in this case, the expression $\frac{2}{3}x + 17$ is already in its simplest form.

Q: What is the final answer?

A: The final answer is $\frac{2}{3}x + 17$ . This is the expression that represents the number of baseball cards Barry has in terms of the number of cards his brother has.

Q: How can we apply this problem to real-world situations?

A: We can apply this problem to real-world situations in various fields, such as finance, economics, and engineering. Understanding fractions and algebraic expressions is crucial in these fields, as it helps us to represent complex relationships and make informed decisions.

Q: What are some common mistakes to avoid when solving this problem?

A: Some common mistakes to avoid when solving this problem include:

Not understanding the concept of fractions and algebraic expressions.
Not following the order of operations (PEMDAS).
Not simplifying the expression.

Q: What are some tips for solving this problem?

A: Some tips for solving this problem include:

Understanding the concept of fractions and algebraic expressions.
Following the order of operations (PEMDAS).
Simplifying the expression.