Representing the Relationship as an Equation

Oct 13, 2025 by recoveryshake.com 35 views

In this problem, we are given the information that Cole's age is 3 years less than his sister Tina's age, denoted as $t$ . We are also told that Cole is 18 years old. Our goal is to find the equation that represents this situation and determine Tina's age.

Representing the Relationship as an Equation

To represent the relationship between Cole's and Tina's ages as an equation, we need to use the given information. Since Cole's age is 3 years less than Tina's age, we can write an equation in the form of $t - 3 = \text{Cole's age}$ .

Substituting Cole's Age into the Equation

We are given that Cole is 18 years old. We can substitute this value into the equation to get:

$t - 3 = 18$

This equation represents the relationship between Cole's and Tina's ages.

Solving for Tina's Age

To find Tina's age, we need to solve the equation for $t$ . We can do this by adding 3 to both sides of the equation:

$t - 3 + 3 = 18 + 3$

This simplifies to:

$t = 21$

Therefore, Tina is 21 years old.

Conclusion

In this problem, we represented the relationship between Cole's and Tina's ages as an equation and solved for Tina's age. We found that the equation that represents this situation is $t - 3 = 18$ , and Tina is 21 years old.

Key Takeaways

To represent the relationship between two variables as an equation, we need to use the given information.
We can substitute values into the equation to solve for the unknown variable.
Solving for the unknown variable involves isolating it on one side of the equation.

Practice Problems

If John's age is 5 years more than his sister Emily's age, and John is 22 years old, which equation represents this situation, and how old is Emily?
If Sarah's age is 2 years less than her brother Michael's age, and Sarah is 15 years old, which equation represents this situation, and how old is Michael?

Answer Key

The equation that represents this situation is $e + 5 = 22$ . Emily is 17 years old.
The equation that represents this situation is $m - 2 = 15$ . Michael is 17 years old.
Frequently Asked Questions (FAQs) About Representing Relationships as Equations ====================================================================================

In this article, we will address some common questions and concerns about representing relationships as equations. Whether you're a student, teacher, or simply someone looking to improve your math skills, this FAQ section is designed to provide you with the information and guidance you need to succeed.

Q: What is the difference between a relationship and an equation?

A: A relationship is a connection or association between two or more variables. An equation, on the other hand, is a mathematical statement that represents a relationship between variables using an equal sign (=). In other words, an equation is a way of expressing a relationship in a mathematical form.

Q: How do I represent a relationship as an equation?

A: To represent a relationship as an equation, you need to follow these steps:

Identify the variables involved in the relationship.
Determine the type of relationship (e.g., addition, subtraction, multiplication, or division).
Write an equation using the variables and the relationship type.
Use the given information to substitute values into the equation.
Solve for the unknown variable.

Q: What is the order of operations when solving an equation?

A: When solving an equation, it's essential to follow the order of operations (PEMDAS):

Parentheses: Evaluate expressions inside parentheses first.
Exponents: Evaluate any exponential expressions next.
Multiplication and Division: Evaluate multiplication and division operations from left to right.
Addition and Subtraction: Finally, evaluate any addition and subtraction operations from left to right.

Q: How do I solve for an unknown variable in an equation?

A: To solve for an unknown variable in an equation, you need to isolate the variable on one side of the equation. This can be done by:

Adding or subtracting the same value to both sides of the equation.
Multiplying or dividing both sides of the equation by the same non-zero value.
Using inverse operations to eliminate the variable.

Q: What is the difference between a linear equation and a non-linear equation?

A: A linear equation is an equation in which the highest power of the variable(s) is 1. Examples of linear equations include:

2x + 3 = 5
x - 2 = 3

A non-linear equation, on the other hand, is an equation in which the highest power of the variable(s) is greater than 1. Examples of non-linear equations include:

x^2 + 2x + 1 = 0
2x^3 - 3x^2 + x + 1 = 0

Q: How do I graph an equation?

A: To graph an equation, you need to follow these steps:

Choose a coordinate system (e.g., Cartesian or polar).
Determine the type of graph (e.g., line, curve, or function).
Use the equation to find the x and y values of key points.
Plot the points on the graph.
Draw a smooth curve through the points to create the graph.

Q: What are some common types of equations?

A: Some common types of equations include:

Linear equations (e.g., 2x + 3 = 5)
Quadratic equations (e.g., x^2 + 2x + 1 = 0)
Polynomial equations (e.g., 2x^3 - 3x^2 + x + 1 = 0)
Rational equations (e.g., 1/x + 2/x^2 = 3/x^3)
Exponential equations (e.g., 2^x = 8)

Conclusion

Representing relationships as equations is a fundamental concept in mathematics. By understanding how to represent relationships as equations, you can solve a wide range of problems and apply mathematical concepts to real-world situations. Whether you're a student, teacher, or simply someone looking to improve your math skills, this FAQ section is designed to provide you with the information and guidance you need to succeed.