Pieter Wrote And Solved An Equation That Models The Number Of Hours It Takes To Dig A Well To A Level Of 72 Feet Below Sea Level.$\[7h - 5(3h - 8) = -72\\]Which Statement Is True About Pieter's Solution?A. It Cannot Be A Fraction Or Decimal

Introduction

In mathematics, equations are used to model real-world problems and represent relationships between variables. Pieter's equation, which models the number of hours it takes to dig a well to a level of 72 feet below sea level, is a classic example of a linear equation. In this article, we will explore Pieter's equation, solve it, and discuss the properties of its solution.

The Equation

The equation is given as:

${7h - 5(3h - 8) = -72}$

This equation represents the relationship between the number of hours it takes to dig a well, denoted by ${h}$, and the depth of the well, which is 72 feet below sea level.

Solving the Equation

To solve the equation, we will use the distributive property to expand the expression inside the parentheses:

${7h - 5(3h - 8) = 7h - 15h + 40 = -72}$

Combining like terms, we get:

${-8h + 40 = -72}$

Subtracting 40 from both sides, we get:

${-8h = -112}$

Dividing both sides by -8, we get:

${h = \frac{-112}{-8} = 14}$

Properties of the Solution

Now that we have solved the equation, let's discuss the properties of the solution. The solution, ${h = 14}$, represents the number of hours it takes to dig a well to a level of 72 feet below sea level.

Statement Analysis

The statement "It cannot be a fraction or decimal" is false. The solution, ${h = 14}$, is an integer, but it can also be expressed as a fraction or decimal. For example, ${h = 14 = \frac{14}{1} = 14.0}$.

Conclusion

In conclusion, Pieter's equation is a linear equation that models the number of hours it takes to dig a well to a level of 72 feet below sea level. The solution to the equation is ${h = 14}$, which represents the number of hours it takes to dig the well. The solution can be expressed as an integer, fraction, or decimal.

Additional Discussion

The equation can be solved using other methods, such as substitution or elimination. However, the distributive property is a useful tool for expanding expressions and simplifying equations.

Real-World Applications

The equation has real-world applications in engineering, construction, and other fields where digging wells or excavations are necessary. The solution to the equation can be used to estimate the time and resources required to complete a project.

Mathematical Concepts

The equation involves several mathematical concepts, including:

• Linear equations: Equations that can be written in the form ${ax + b = c}$, where ${a}$, ${b}$, and ${c}$ are constants.
• Distributive property: A property that states that for any numbers ${a}$, ${b}$, and ${c}$, ${a(b + c) = ab + ac}$.
• Combining like terms: A process of combining terms that have the same variable and coefficient.

Conclusion

$$

Introduction

In our previous article, we explored Pieter's equation, which models the number of hours it takes to dig a well to a level of 72 feet below sea level. We solved the equation and discussed the properties of its solution. In this article, we will answer some frequently asked questions about Pieter's equation.

Q&A

Q: What is Pieter's equation?

A: Pieter's equation is a linear equation that models the number of hours it takes to dig a well to a level of 72 feet below sea level. The equation is given as:

${7h - 5(3h - 8) = -72}$

Q: How do I solve Pieter's equation?

A: To solve Pieter's equation, you can use the distributive property to expand the expression inside the parentheses, combine like terms, and then isolate the variable ${h}$.

Q: What is the solution to Pieter's equation?

A: The solution to Pieter's equation is ${h = 14}$, which represents the number of hours it takes to dig a well to a level of 72 feet below sea level.

Q: Can the solution to Pieter's equation be a fraction or decimal?

A: Yes, the solution to Pieter's equation can be expressed as a fraction or decimal. For example, ${h = 14 = \frac{14}{1} = 14.0}$.

Q: What are some real-world applications of Pieter's equation?

A: Pieter's equation has real-world applications in engineering, construction, and other fields where digging wells or excavations are necessary. The solution to the equation can be used to estimate the time and resources required to complete a project.

Q: What mathematical concepts are involved in solving Pieter's equation?

A: The equation involves several mathematical concepts, including linear equations, distributive property, and combining like terms.

Q: Can I use other methods to solve Pieter's equation?

A: Yes, you can use other methods, such as substitution or elimination, to solve Pieter's equation. However, the distributive property is a useful tool for expanding expressions and simplifying equations.

Q: What is the significance of Pieter's equation in mathematics?

A: Pieter's equation is a classic example of a linear equation and demonstrates the importance of using mathematical concepts, such as distributive property and combining like terms, to solve equations.

Conclusion

In conclusion, Pieter's equation is a linear equation that models the number of hours it takes to dig a well to a level of 72 feet below sea level. The solution to the equation is ${h = 14}$, which represents the number of hours it takes to dig the well. The equation has real-world applications and involves several mathematical concepts, including linear equations, distributive property, and combining like terms.

Additional Resources

For more information on Pieter's equation and other mathematical concepts, please refer to the following resources:

• Math textbooks: Many math textbooks, such as "Algebra and Trigonometry" by Michael Sullivan, cover linear equations and other mathematical concepts.
• Online resources: Websites, such as Khan Academy and Mathway, offer interactive lessons and exercises on linear equations and other mathematical concepts.
• Mathematical software: Software, such as Mathematica and Maple, can be used to solve linear equations and other mathematical problems.

Conclusion

In conclusion, Pieter's equation is a linear equation that models the number of hours it takes to dig a well to a level of 72 feet below sea level. The solution to the equation is ${h = 14}$, which represents the number of hours it takes to dig the well. The equation has real-world applications and involves several mathematical concepts, including linear equations, distributive property, and combining like terms.