Alexia Spent 3 Minutes Working On Each Of Her Math Problems And 4 Minutes On Each Of Her Science Problems. Her Homework Took Her More Than 60 Minutes To Complete. The Boundary Line For The Inequality $3x + 4y = 60$ Is Shown.Which Statement

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Introduction

Alexia, a diligent student, spent a significant amount of time working on her math and science homework. She devoted 3 minutes to each math problem and 4 minutes to each science problem. The total time she spent on her homework exceeded 60 minutes. In this article, we will analyze the situation using a mathematical inequality and determine which statement is true.

The Inequality

The inequality 3x+4y=603x + 4y = 60 represents the total time Alexia spent on her homework. Here, xx represents the number of math problems she solved, and yy represents the number of science problems she solved. The boundary line for this inequality is shown in the graph below.

Graphical Representation

The graph below represents the inequality 3x+4y=603x + 4y = 60. The boundary line is a straight line that passes through the points (0, 15) and (20, 0).

### Graphical Representation

![Graphical Representation](https://example.com/graphical-representation.png)

Analyzing the Statements

There are three statements that we need to analyze:

  1. Alexia solved at least 15 math problems.
  2. Alexia solved at most 20 science problems.
  3. Alexia solved more than 20 math problems.

Statement 1: Alexia Solved at Least 15 Math Problems

To determine if this statement is true, we need to find the minimum value of xx that satisfies the inequality 3x+4y=603x + 4y = 60. We can do this by setting y=0y = 0 and solving for xx.

### Statement 1: Alexia Solved at Least 15 Math Problems

*   Set $y = 0$
*   Solve for $x$: $3x = 60$
*   $x = 20$
*   Since $x$ must be an integer, the minimum value of $x$ is 20.
*   Therefore, Alexia solved at least 20 math problems, not 15.

Statement 2: Alexia Solved at Most 20 Science Problems

To determine if this statement is true, we need to find the maximum value of yy that satisfies the inequality 3x+4y=603x + 4y = 60. We can do this by setting x=0x = 0 and solving for yy.

### Statement 2: Alexia Solved at Most 20 Science Problems

*   Set $x = 0$
*   Solve for $y$: $4y = 60$
*   $y = 15$
*   Since $y$ must be an integer, the maximum value of $y$ is 15.
*   Therefore, Alexia solved at most 15 science problems, not 20.

Statement 3: Alexia Solved More Than 20 Math Problems

To determine if this statement is true, we need to find the minimum value of xx that satisfies the inequality 3x+4y=603x + 4y = 60 and x>20x > 20. We can do this by setting y=0y = 0 and solving for xx.

### Statement 3: Alexia Solved More Than 20 Math Problems

*   Set $y = 0$
*   Solve for $x$: $3x = 60$
*   $x = 20$
*   Since $x$ must be greater than 20, this statement is false.

Conclusion

In conclusion, Alexia solved at least 20 math problems, at most 15 science problems, and not more than 20 math problems. Therefore, the correct statement is that Alexia solved at least 20 math problems.

References

Further Reading

Appendix

The following is a list of mathematical concepts and formulas used in this article:

Introduction

In our previous article, we analyzed Alexia's homework dilemma using a mathematical inequality. We determined that Alexia solved at least 20 math problems, at most 15 science problems, and not more than 20 math problems. In this article, we will answer some frequently asked questions related to this topic.

Q&A

Q1: What is the boundary line for the inequality 3x+4y=603x + 4y = 60?

A1: The boundary line for the inequality 3x+4y=603x + 4y = 60 is a straight line that passes through the points (0, 15) and (20, 0).

Q2: How many math problems did Alexia solve?

A2: Alexia solved at least 20 math problems.

Q3: How many science problems did Alexia solve?

A3: Alexia solved at most 15 science problems.

Q4: Is it possible for Alexia to solve more than 20 math problems?

A4: No, it is not possible for Alexia to solve more than 20 math problems.

Q5: What is the minimum value of xx that satisfies the inequality 3x+4y=603x + 4y = 60?

A5: The minimum value of xx that satisfies the inequality 3x+4y=603x + 4y = 60 is 20.

Q6: What is the maximum value of yy that satisfies the inequality 3x+4y=603x + 4y = 60?

A6: The maximum value of yy that satisfies the inequality 3x+4y=603x + 4y = 60 is 15.

Q7: Can we use the inequality 3x+4y=603x + 4y = 60 to determine the number of math and science problems Alexia solved?

A7: Yes, we can use the inequality 3x+4y=603x + 4y = 60 to determine the number of math and science problems Alexia solved.

Q8: What is the significance of the inequality 3x+4y=603x + 4y = 60 in this context?

A8: The inequality 3x+4y=603x + 4y = 60 represents the total time Alexia spent on her homework.

Q9: Can we use the graphical representation of the inequality 3x+4y=603x + 4y = 60 to determine the number of math and science problems Alexia solved?

A9: Yes, we can use the graphical representation of the inequality 3x+4y=603x + 4y = 60 to determine the number of math and science problems Alexia solved.

Q10: What is the relationship between the inequality 3x+4y=603x + 4y = 60 and the number of math and science problems Alexia solved?

A10: The inequality 3x+4y=603x + 4y = 60 represents the total time Alexia spent on her homework, which is related to the number of math and science problems she solved.

Conclusion

In conclusion, we have answered some frequently asked questions related to Alexia's homework dilemma using a mathematical inequality. We hope this article has provided valuable insights into the topic.

References

Further Reading

Appendix

The following is a list of mathematical concepts and formulas used in this article:

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