Analyzing Textbook Sales Using Basic Algebra

Bookstore managers often turn to mathematics to analyze sales data and gain insights into popular subjects. This article delves into a real-life scenario faced by a textbook store, where the combined sales of history and chemistry textbooks were 392. Intriguingly, the number of history textbooks sold was three times the number of chemistry textbooks sold. This case study will employ basic algebra to unravel the mystery behind these sales figures.

Setting Up the Equations

Let's translate this scenario into mathematical equations. If we denote the number of history textbooks sold by H, and the number of chemistry textbooks sold by C, we can represent the given information as:

By substituting the second equation into the first equation, we can solve for C, the number of chemistry textbooks sold.

Solving the Equations

Substituting H 3C into the first equation:

H C 392

3C C 392

4C 392

To isolate C, we divide both sides by 4:

4C/4 392/4

C 98

The number of chemistry textbooks sold is 98. Now, to find the number of history textbooks sold, we use the equation:

H 3C

H 3 98

H 294

Thus, the textbook store sold 294 history textbooks and 98 chemistry textbooks.

Revisiting the Original Data

A revisit to the original data reveals an interesting twist. The store sold a combined total of 416 math and sociology textbooks in a week. This time, the relationship between the two types of textbooks is

M 3S

M S 416

Again, using the substitution method:

M S 416

3S S 416

4S 416

Dividing both sides by 4:

S 416/4

S 104

Therefore, the number of sociology textbooks sold was 104. Since the number of math textbooks sold was three times that of sociology textbooks:

M 3 104

M 312

So, the textbook store sold 104 sociology textbooks and 312 math textbooks last week.

Conclusion

Mathematics, particularly algebra, plays a crucial role in analyzing sales data. By breaking down complex sales figures into equations, we can gain clear insights into what subjects are in high demand. This exercise, though seemingly simple, underscores the importance of mathematical literacy in the modern business environment. For intermediate students and managers alike, mastering these basic algebra skills can significantly enhance decision-making processes and sales strategies.