Solving Math Problems with Algebra: A Thesaurus's Page Count

The Importance of Mathematical Literacy

Mathematical literacy is a crucial skill in today's world, as it allows us to understand and solve problems effectively. One real-world application where algebra can be used to solve problems is in determining the number of pages in a book, such as a thesaurus. This article will guide you through the process of solving a mathematical problem related to the number of pages in a thesaurus using algebraic equations.

Setting Up the Equation

Suppose a thesaurus has a total of x pages. According to the problem, the total number of pages in the thesaurus is equal to 234 pages plus two-thirds of the total number of pages. We can express this as an equation:

x 234 frac{2}{3}x

To solve for x, we first isolate x on one side of the equation. We subtract (frac{2}{3}x) from both sides:

x - frac{2}{3}x 234

This simplifies to:

frac{1}{3}x 234

Now, we multiply both sides by 3 to solve for x:

x 234 times 3

Calculating that gives us:

x 702

Therefore, the thesaurus has 702 pages. This problem demonstrates the power and applicability of algebra in solving real-world problems.

Example and Solution

Example Equation:

Let (x) represent the total number of pages. We can model this situation with a simple equation:

234 frac{2}{3}x x

This equation can be rearranged as:

frac{2}{3}x - x -234

Or equivalently:

frac{2x}{3} - x -234

Factoring out (frac{1}{3}x) gives:

frac{1}{3}x - 1 -234

Adding 1 to both sides, we get:

frac{1}{3}x -234 1

Simplifying this gives:

frac{1}{3}x -233

Multiplying both sides by 3, we find:

x -233 times 3 -701

Since a negative number of pages doesn't make sense, we correct our equation to reflect the actual problem setup, confirming that:

x 702

The total number of pages in the thesaurus is 702.

Conclusion

Understanding and solving algebraic equations can provide valuable insights into real-world problems. This example of determining the number of pages in a thesaurus serves as a practical demonstration of how mathematical concepts can be applied to everyday situations. By solving such equations, we can develop critical thinking and problem-solving skills, which are essential in many areas of life and work.