Model With Mathematics.Gim Made $9 Per Hour Working As A Lifeguard. How Many Hours Did He Work This Week If His Weekly Pay Before Deductions Was $288? Define A Variable And Write An Equation. Solve The Equation.Write An Equation Using X As

Feb 28, 2025 by ADMIN 242 views

**Model with Mathematics: Solving a Real-World Problem**

Introduction

Mathematics is an essential tool for solving real-world problems. In this article, we will use mathematical concepts to model a scenario and find a solution. We will define a variable, write an equation, and solve it to find the answer.

Problem Statement

Gim made $9 per hour working as a lifeguard. How many hours did he work this week if his weekly pay before deductions was $288?

Defining a Variable

Let's define a variable to represent the number of hours Gim worked. We will use the variable x to represent the number of hours.

Writing an Equation

We know that Gim made $9 per hour, and his weekly pay before deductions was $288. We can write an equation to represent this situation:

9x = 288

In this equation, 9x represents the total amount of money Gim made, and 288 represents his weekly pay before deductions.

Solving the Equation

To solve the equation, we need to isolate the variable x. We can do this by dividing both sides of the equation by 9:

x = 288 ÷ 9

x = 32

Therefore, Gim worked 32 hours this week.

Interpretation

In this problem, we used mathematical concepts to model a real-world scenario. We defined a variable, wrote an equation, and solved it to find the answer. This is a common approach in mathematics, where we use mathematical models to solve problems and make predictions.

Real-World Applications

This problem has real-world applications in various fields, such as finance, economics, and business. For example, in finance, we use mathematical models to calculate interest rates, investment returns, and risk management. In economics, we use mathematical models to analyze economic systems, predict economic trends, and make policy decisions. In business, we use mathematical models to optimize production, manage supply chains, and make strategic decisions.

Conclusion

In this article, we used mathematical concepts to model a real-world problem and find a solution. We defined a variable, wrote an equation, and solved it to find the answer. This is a common approach in mathematics, where we use mathematical models to solve problems and make predictions. We hope this article has provided a clear understanding of how mathematics can be used to solve real-world problems.

Additional Examples

Here are some additional examples of how mathematics can be used to solve real-world problems:

Finance: A bank offers a 5% interest rate on a savings account. If you deposit $1000, how much will you have after 1 year?
Economics: A country's GDP grows at a rate of 3% per year. If the GDP is $100 billion, what will it be after 5 years?
Business: A company produces 1000 units of a product per day. If the product sells for $20 per unit, what is the daily revenue?

These are just a few examples of how mathematics can be used to solve real-world problems. The possibilities are endless, and the use of mathematics is essential in many fields.

Glossary

Variable: A symbol or expression that represents a value that can change.
Equation: A statement that expresses the equality of two mathematical expressions.
Solution: A value that satisfies an equation.

References

Mathematics for Dummies by Mary Jane Sterling
Mathematics: A Very Short Introduction by Timothy Gowers
Real-World Math by David A. Adler

Introduction

In our previous article, we used mathematical concepts to model a real-world problem and find a solution. We defined a variable, wrote an equation, and solved it to find the answer. In this article, we will provide a Q&A section to further clarify the concepts and provide additional examples.

Q&A

Q: What is a variable in mathematics?

A: A variable is a symbol or expression that represents a value that can change. In the example we used earlier, x represented the number of hours Gim worked.

Q: How do I know when to use a variable?

A: You use a variable when you are trying to represent a value that can change. For example, if you are trying to calculate the cost of a product that can vary in price, you would use a variable to represent the price.

Q: What is an equation in mathematics?

A: An equation is a statement that expresses the equality of two mathematical expressions. In the example we used earlier, 9x = 288 was an equation that expressed the equality of the total amount of money Gim made and his weekly pay before deductions.

Q: How do I know when to use an equation?

A: You use an equation when you are trying to solve a problem that involves a relationship between two or more values. For example, if you are trying to calculate the cost of a product that depends on the price and the quantity sold, you would use an equation to represent the relationship.

Q: What is a solution in mathematics?

A: A solution is a value that satisfies an equation. In the example we used earlier, x = 32 was a solution to the equation 9x = 288.

Q: How do I know when to use a solution?

A: You use a solution when you are trying to find a value that satisfies an equation. For example, if you are trying to find the number of hours Gim worked, you would use a solution to the equation 9x = 288.

Q: What are some common types of equations?

A: Some common types of equations include:

Linear equations: Equations that can be written in the form ax + b = c, where a, b, and c are constants.
Quadratic equations: Equations that can be written in the form ax^2 + bx + c = 0, where a, b, and c are constants.
Exponential equations: Equations that involve exponential functions, such as 2^x = 8.

Q: How do I solve a linear equation?

A: To solve a linear equation, you can use the following steps:

Add or subtract the same value to both sides of the equation to isolate the variable.
Multiply or divide both sides of the equation by the same value to isolate the variable.
Use inverse operations to isolate the variable.

Q: How do I solve a quadratic equation?

A: To solve a quadratic equation, you can use the following steps:

Factor the equation, if possible.
Use the quadratic formula: x = (-b ± √(b^2 - 4ac)) / 2a.
Use inverse operations to isolate the variable.

Q: How do I solve an exponential equation?

A: To solve an exponential equation, you can use the following steps:

Use logarithms to rewrite the equation in a form that can be solved.
Use inverse operations to isolate the variable.

Conclusion

In this article, we provided a Q&A section to further clarify the concepts and provide additional examples. We hope this article has provided a clear understanding of how mathematics can be used to solve real-world problems.