Master Algebra with this Step-by-Step Word Problem Solution

Master Algebra with this Step-by-Step Word Problem Solution

Table of Contents

1. Introduction
2. About the Problem
3. Understanding Variables
4. Constructing the Equation
5. Solving the Equation
6. Interpreting the Solution
7. Real-Life Applications of Algebra
8. Additional Math Help
9. Conclusion

Introduction

In this article, we will explore a classic algebra word problem that involves finding the number of quarters and dimes given a certain amount of change. We will walk through the problem step by step, explaining the concepts and techniques used to solve it. By the end of this article, You will have a better understanding of how algebra can be applied to real-life situations and how to approach word problems effectively.

About the Problem

The problem states that you have $5.50 in change, consisting of only quarters and dimes. It also mentions that you have three times the number of dimes than quarters. The task is to determine the number of dimes and quarters you have.

Understanding Variables

To solve the problem, we first need to identify a variable to represent the unknown quantities. In this case, let's use "x" to represent the number of quarters. Since we have three times the number of dimes than quarters, the number of dimes would be 3x.

Constructing the Equation

Next, we construct an equation using the information given. We need to consider the monetary value of the coins. A quarter is equivalent to $0.25, so the value of the quarters can be expressed as 0.25x. Similarly, a dime is worth $0.10, so the value of the dimes is 0.10(3x). The equation can be written as:

0.25x + 0.10(3x) = 5.50

Solving the Equation

To solve the equation, we simplify and combine like terms. Adding the values, we get 0.25x + 0.30x = 5.50. Combining the x terms gives us 0.55x = 5.50. Dividing both sides by 0.55, we find that x = 10.

Interpreting the Solution

The value of x represents the number of quarters, so we have 10 quarters. Since there are three times as many dimes as quarters, we have 30 dimes. Therefore, the solution to the problem is 10 quarters and 30 dimes.

Real-Life Applications of Algebra

Although this word problem may not have direct practical applications, it is a great illustration of how algebra can be used to solve various real-life problems. Algebra is commonly used in areas such as finance, engineering, and sciences to analyze and solve complex situations.

Additional Math Help

If you need further assistance with algebra or other math topics, consider exploring online math courses and programs. There are various resources available that can provide comprehensive math instruction and support.

Conclusion

Solving algebra word problems requires the application of variables, equations, and problem-solving techniques. By understanding the steps involved in solving a problem like the one presented here, you will develop important problem-solving skills that can be applied to a wide range of situations. Algebra is not only a subject taught in schools but also a valuable tool used in real life for practical problem-solving.