Solving Word Problems Involving Three Numbers Using Algebra

In mathematics and algebra, solving word problems involving three numbers is a common task that helps in developing problem-solving skills. This article will guide you through solving such problems step-by-step using algebraic techniques.

Problem 1: The Sum of Three Numbers is 89

Let's denote the first number as x. According to the problem:

The second number is 6x. The third number is 6x - 15. The sum of the three numbers is given as 89.

We can represent this with the equation:

x   6x   (6x - 15)  89

Now, let's simplify this equation:

x   6x   6x - 15  89
13x - 15  89
13x  104
x  104 / 13  8

Thus, the first number is 8. To verify:

Second number: 6x 6 × 8 48 Third number: 6x - 15 48 - 15 33

The sum of 8 48 33 is indeed 89, confirming that the first number is 8.

Problem 2: The Sum of Three Numbers is 112

Let's denote the first number as a. According to the problem:

The second number is 5a. The third number is 5a - 20. The sum of the three numbers is given as 112.

We can represent this with the equation:

a   5a   (5a - 20)  112

Now, let's simplify this equation:

a   5a   5a - 20  112
11a - 20  112
11a  132
a  132 / 11  12

Thus, the first number is 12. To verify:

The second number: 5a 5 × 12 60 The third number: 5a - 20 60 - 20 40

The sum of 12 60 40 is indeed 112, confirming that the first number is 12.

Problem 3: Understanding Algebraic Equations and Problem-Solving Techniques

Algebra is a powerful tool for solving real-world problems. By using algebra, we can:

Translate word problems into mathematical expressions. Simplify and solve these expressions to find unknown values. Verify the solutions to ensure their accuracy.

Understanding and practicing these techniques can help improve your mathematical skills, making it easier to solve a wide range of complex problems.

Conclusion

Solving word problems involving three numbers using algebra is a fundamental skill that can be applied in various real-life situations, such as financial planning, scientific research, and even everyday decision-making. By following these steps and practicing similar problems, you can enhance your problem-solving abilities and develop a deeper understanding of algebra.