Hiroshi Spends 30 Minutes On History Homework, 60 Minutes On English Homework, And X X X Minutes On Math Homework. One Fourth Of His Total Homework Time Is Spent On Math. Which Equation Can Be Used To Find The Amount Of Time Hiroshi Spends On

Understanding the Problem

Hiroshi spends a significant amount of time on his homework, and we need to determine the amount of time he spends on math homework. We are given that he spends 30 minutes on history homework, 60 minutes on English homework, and an unknown amount of time, denoted as $x$ minutes, on math homework. Additionally, we know that one fourth of his total homework time is spent on math.

Breaking Down the Information

Let's break down the information we have:

• Hiroshi spends 30 minutes on history homework.
• Hiroshi spends 60 minutes on English homework.
• Hiroshi spends $x$ minutes on math homework.
• One fourth of his total homework time is spent on math.

Formulating the Equation

We can start by finding the total amount of time Hiroshi spends on his homework. Let's denote this as $T$. We know that $T$ is the sum of the time spent on history, English, and math homework.

$$T = 30 + 60 + x$$

Simplifying the equation, we get:

$$T = 90 + x$$

Now, we are told that one fourth of his total homework time is spent on math. This means that the time spent on math is equal to one fourth of the total time spent on homework. We can write this as:

$$\frac{1}{4}T = x$$

Substituting the expression for $T$ from the previous equation, we get:

$$\frac{1}{4}(90 + x) = x$$

Solving the Equation

To solve for $x$, we can start by multiplying both sides of the equation by 4 to eliminate the fraction:

$$90 + x = 4x$$

Next, we can subtract $x$ from both sides to get:

$$90 = 3x$$

Finally, we can divide both sides by 3 to solve for $x$:

$$x = 30$$

Conclusion

In conclusion, the equation that can be used to find the amount of time Hiroshi spends on math homework is:

$$\frac{1}{4}(90 + x) = x$$

Solving this equation, we find that Hiroshi spends 30 minutes on math homework.

Key Takeaways

• The total amount of time Hiroshi spends on his homework is $T = 90 + x$.
• One fourth of his total homework time is spent on math, which can be expressed as $\frac{1}{4}T = x$.
• Solving the equation $\frac{1}{4}(90 + x) = x$, we find that Hiroshi spends 30 minutes on math homework.

Real-World Applications

This problem can be applied to real-world scenarios where we need to allocate time for different tasks. For example, if you are planning a project and need to allocate time for different tasks, you can use this equation to determine the amount of time you need to spend on each task.

Common Mistakes

When solving this problem, it's easy to get confused and make mistakes. Here are some common mistakes to avoid:

• Not simplifying the equation correctly.
• Not solving for the correct variable.
• Not checking the units of the answer.

Tips and Tricks

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

• Make sure to read the problem carefully and understand what is being asked.
• Break down the problem into smaller steps and solve each step separately.
• Check your units of measurement to ensure that they are correct.

Additional Resources

If you need additional help or resources to solve this problem, here are some additional resources you can use:

• Online math resources, such as Khan Academy or Mathway.
• Math textbooks or workbooks.
• Online forums or discussion groups.

Final Thoughts

In conclusion, the equation that can be used to find the amount of time Hiroshi spends on math homework is:

$$\frac{1}{4}(90 + x) = x$$

Q: What is the total amount of time Hiroshi spends on his homework?

A: The total amount of time Hiroshi spends on his homework is $T = 90 + x$, where $x$ is the amount of time he spends on math homework.

Q: How much time does Hiroshi spend on math homework?

A: To find the amount of time Hiroshi spends on math homework, we need to solve the equation $\frac{1}{4}(90 + x) = x$. Solving this equation, we find that Hiroshi spends 30 minutes on math homework.

Q: What is the equation that can be used to find the amount of time Hiroshi spends on math homework?

A: The equation that can be used to find the amount of time Hiroshi spends on math homework is:

$$\frac{1}{4}(90 + x) = x$$

Q: How can I apply this problem to real-world scenarios?

A: This problem can be applied to real-world scenarios where we need to allocate time for different tasks. For example, if you are planning a project and need to allocate time for different tasks, you can use this equation to determine the amount of time you need to spend on each task.

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

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

• Not simplifying the equation correctly.
• Not solving for the correct variable.
• Not checking the units of the answer.

Q: What are some tips and tricks to help me solve this problem?

A: Some tips and tricks to help you solve this problem include:

• Make sure to read the problem carefully and understand what is being asked.
• Break down the problem into smaller steps and solve each step separately.
• Check your units of measurement to ensure that they are correct.

Q: Where can I find additional resources to help me solve this problem?

A: If you need additional help or resources to solve this problem, here are some additional resources you can use:

• Online math resources, such as Khan Academy or Mathway.
• Math textbooks or workbooks.
• Online forums or discussion groups.

Q: Can I use this equation to find the amount of time Hiroshi spends on other subjects?

A: Yes, you can use this equation to find the amount of time Hiroshi spends on other subjects. For example, if you want to find the amount of time Hiroshi spends on history homework, you can use the equation $T = 90 + x$ and substitute the value of $x$ with the amount of time Hiroshi spends on math homework.

Q: How can I check my answer to make sure it is correct?

A: To check your answer, you can plug the value of $x$ back into the original equation and make sure that it is true. For example, if you find that Hiroshi spends 30 minutes on math homework, you can plug this value back into the equation $\frac{1}{4}(90 + x) = x$ and make sure that it is true.

Q: What is the importance of checking units of measurement?

A: Checking units of measurement is important because it ensures that your answer is correct and makes sense in the context of the problem. For example, if you find that Hiroshi spends 30 minutes on math homework, you can check that the units of measurement are correct by making sure that the answer is in minutes.

Q: Can I use this equation to solve other problems involving time and algebra?

A: Yes, you can use this equation to solve other problems involving time and algebra. For example, if you have a problem that involves finding the amount of time it takes to complete a task, you can use this equation to solve it.

Q: How can I apply this problem to real-world scenarios involving time and algebra?

A: This problem can be applied to real-world scenarios involving time and algebra, such as:

• Finding the amount of time it takes to complete a project.
• Determining the amount of time it takes to travel from one place to another.
• Calculating the amount of time it takes to complete a task.

Q: What are some common applications of this problem in real-world scenarios?

A: Some common applications of this problem in real-world scenarios include:

• Project management: Finding the amount of time it takes to complete a project.
• Transportation: Determining the amount of time it takes to travel from one place to another.
• Business: Calculating the amount of time it takes to complete a task.

Q: Can I use this equation to solve problems involving other variables?

A: Yes, you can use this equation to solve problems involving other variables. For example, if you have a problem that involves finding the amount of time it takes to complete a task, you can use this equation to solve it.

Q: How can I modify this equation to solve problems involving other variables?

A: To modify this equation to solve problems involving other variables, you can substitute the variable with the new variable and solve the equation. For example, if you have a problem that involves finding the amount of time it takes to complete a task, you can substitute the variable with the new variable and solve the equation.