The Sum Of Bobbi's And Dan's Heights Is 130 Inches. Dan's Height Subtracted From 3 Times Bobbi's Height Is 118 Inches. What Are Bobbi's And Dan's Heights In Inches?1. Let B B B = Bobbi's Height And Let D D D = Dan's Height. Fill In The

Introduction

In this article, we will delve into a mathematical puzzle involving the heights of two individuals, Bobbi and Dan. We will use algebraic equations to represent the given information and solve for the heights of Bobbi and Dan. This problem is a great example of how algebra can be used to model real-world scenarios and solve for unknown values.

Problem Statement

Let $b$ = Bobbi's height and let $d$ = Dan's height. The sum of Bobbi's and Dan's heights is 130 inches, which can be represented by the equation:

$$b + d = 130$$

Additionally, we are given the information that Dan's height subtracted from 3 times Bobbi's height is 118 inches, which can be represented by the equation:

$$3b - d = 118$$

Solving the System of Equations

To solve for the heights of Bobbi and Dan, we can use the method of substitution or elimination. In this case, we will use the elimination method to eliminate one of the variables.

First, we can add the two equations together to eliminate the variable $d$:

$$b + d + 3b - d = 130 + 118$$

Simplifying the equation, we get:

$$4b = 248$$

Dividing both sides by 4, we get:

$$b = 62$$

Now that we have found the value of $b$, we can substitute it into one of the original equations to solve for $d$. We will use the first equation:

$$b + d = 130$$

Substituting $b = 62$, we get:

$$62 + d = 130$$

Subtracting 62 from both sides, we get:

$$d = 68$$

Conclusion

In this article, we used algebraic equations to represent the given information and solve for the heights of Bobbi and Dan. We found that Bobbi's height is 62 inches and Dan's height is 68 inches. This problem is a great example of how algebra can be used to model real-world scenarios and solve for unknown values.

Discussion

This problem can be used to teach students about the importance of algebra in real-world applications. It can also be used to demonstrate the concept of systems of equations and how to solve them using the elimination method.

Real-World Applications

This problem can be used in a variety of real-world applications, such as:

• Medical Research: In medical research, it is often necessary to measure the heights of individuals in order to study the effects of height on various health outcomes.
• Sports: In sports, it is often necessary to measure the heights of athletes in order to determine their eligibility for certain competitions.
• Architecture: In architecture, it is often necessary to measure the heights of buildings in order to determine their structural integrity.

Mathematical Concepts

This problem involves the following mathematical concepts:

• Systems of Equations: This problem involves solving a system of two linear equations with two variables.
• Elimination Method: This problem involves using the elimination method to solve the system of equations.
• Algebraic Manipulation: This problem involves using algebraic manipulation to simplify the equations and solve for the unknown values.

Tips and Tricks

Here are some tips and tricks for solving this problem:

• Read the problem carefully: Make sure to read the problem carefully and understand what is being asked.
• Use algebraic manipulation: Use algebraic manipulation to simplify the equations and solve for the unknown values.
• Check your work: Make sure to check your work by plugging the values back into the original equations.

Conclusion

In conclusion, this problem is a great example of how algebra can be used to model real-world scenarios and solve for unknown values. It involves the use of systems of equations, the elimination method, and algebraic manipulation. By following the tips and tricks outlined in this article, students can learn how to solve this problem and apply the concepts to real-world applications.