At The Gym, Jasper Was Able To Bench Press 224 Pounds, Which Was $\frac{7}{8}$ Of The Weight That Balin Was Able To Bench Press. Which Shows The Correct Equation And Value Of $x$, The Weight That Balin Could Bench Press?A.

Understanding the Problem

In a recent gym session, Jasper was able to bench press 224 pounds, which was $\frac{7}{8}$ of the weight that Balin was able to bench press. We are tasked with finding the correct equation and value of $x$, the weight that Balin could bench press.

Setting Up the Equation

Let's denote Balin's bench press weight as $x$. Since Jasper's bench press weight is $\frac{7}{8}$ of Balin's, we can set up the following equation:

$$\frac{7}{8}x = 224$$

Solving for x

To solve for $x$, we can multiply both sides of the equation by $\frac{8}{7}$, which is the reciprocal of $\frac{7}{8}$.

$$\frac{8}{7} \cdot \frac{7}{8}x = \frac{8}{7} \cdot 224$$

This simplifies to:

$$x = \frac{8}{7} \cdot 224$$

Calculating the Value of x

Now, let's calculate the value of $x$.

$$x = \frac{8}{7} \cdot 224$$

$$x = 256$$

Conclusion

Therefore, the correct equation is $\frac{7}{8}x = 224$, and the value of $x$, the weight that Balin could bench press, is 256 pounds.

Why is this Problem Important?

This problem is important because it demonstrates the application of fractions and algebraic equations in real-world scenarios. In this case, we used fractions to represent the relationship between Jasper's and Balin's bench press weights, and algebraic equations to solve for the unknown value of $x$.

Real-World Applications

This problem has real-world applications in various fields, such as:

• Sports: In sports, understanding fractions and algebraic equations can help athletes and coaches analyze performance data and make informed decisions.
• Science: In science, fractions and algebraic equations are used to model and analyze complex systems, such as population growth and chemical reactions.
• Finance: In finance, fractions and algebraic equations are used to calculate interest rates, investment returns, and other financial metrics.

Tips and Tricks

Here are some tips and tricks to help you solve problems like this:

• Read the problem carefully: Make sure you understand what the problem is asking for.
• Use fractions and algebraic equations: Fractions and algebraic equations are powerful tools for solving problems involving ratios and proportions.
• Check your work: Always check your work to ensure that your solution is correct.

Common Mistakes

Here are some common mistakes to avoid when solving problems like this:

• Not reading the problem carefully: Failing to read the problem carefully can lead to incorrect solutions.
• Not using fractions and algebraic equations: Failing to use fractions and algebraic equations can make it difficult to solve problems involving ratios and proportions.
• Not checking your work: Failing to check your work can lead to incorrect solutions.
  Frequently Asked Questions (FAQs) =====================================

Q: What is the relationship between Jasper's and Balin's bench press weights?

A: Jasper's bench press weight is $\frac{7}{8}$ of Balin's bench press weight.

Q: How do I set up the equation to solve for Balin's bench press weight?

A: To set up the equation, let $x$ represent Balin's bench press weight. Then, since Jasper's bench press weight is $\frac{7}{8}$ of Balin's, we can write the equation as:

$$\frac{7}{8}x = 224$$

Q: How do I solve for x in the equation $\frac{7}{8}x = 224$?

A: To solve for $x$, we can multiply both sides of the equation by $\frac{8}{7}$, which is the reciprocal of $\frac{7}{8}$.

$$\frac{8}{7} \cdot \frac{7}{8}x = \frac{8}{7} \cdot 224$$

This simplifies to:

$$x = \frac{8}{7} \cdot 224$$

Q: What is the value of x, the weight that Balin could bench press?

A: The value of $x$ is 256 pounds.

Q: Why is it important to check my work when solving problems like this?

A: Checking your work is important to ensure that your solution is correct. In this case, if we had not checked our work, we may have arrived at an incorrect solution.

Q: What are some real-world applications of fractions and algebraic equations?

A: Fractions and algebraic equations have many real-world applications, including:

• Sports: In sports, understanding fractions and algebraic equations can help athletes and coaches analyze performance data and make informed decisions.
• Science: In science, fractions and algebraic equations are used to model and analyze complex systems, such as population growth and chemical reactions.
• Finance: In finance, fractions and algebraic equations are used to calculate interest rates, investment returns, and other financial metrics.

Q: What are some tips and tricks for solving problems like this?

A: Here are some tips and tricks to help you solve problems like this:

• Read the problem carefully: Make sure you understand what the problem is asking for.
• Use fractions and algebraic equations: Fractions and algebraic equations are powerful tools for solving problems involving ratios and proportions.
• Check your work: Always check your work to ensure that your solution is correct.

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

A: Here are some common mistakes to avoid when solving problems like this:

• Not reading the problem carefully: Failing to read the problem carefully can lead to incorrect solutions.
• Not using fractions and algebraic equations: Failing to use fractions and algebraic equations can make it difficult to solve problems involving ratios and proportions.
• Not checking your work: Failing to check your work can lead to incorrect solutions.

Q: Can I use a calculator to solve problems like this?

A: Yes, you can use a calculator to solve problems like this. However, it's always a good idea to check your work by hand to ensure that your solution is correct.

Q: How do I know if I have solved the problem correctly?

A: To know if you have solved the problem correctly, make sure to:

• Read the problem carefully: Make sure you understand what the problem is asking for.
• Use fractions and algebraic equations: Fractions and algebraic equations are powerful tools for solving problems involving ratios and proportions.
• Check your work: Always check your work to ensure that your solution is correct.

Q: Can I use this method to solve other problems involving ratios and proportions?

A: Yes, you can use this method to solve other problems involving ratios and proportions. Just remember to:

• Read the problem carefully: Make sure you understand what the problem is asking for.
• Use fractions and algebraic equations: Fractions and algebraic equations are powerful tools for solving problems involving ratios and proportions.
• Check your work: Always check your work to ensure that your solution is correct.