Solving a Mathematical Problem: The Cost of Textbooks and Exercise Books
Consider the situation of a bookseller who purchased a certain number of textbooks and exercise books. The price of a textbook is four times that of an exercise book. Given that the bookseller spent $25,000 on textbooks and $10,000 on exercise books, and the total number of items purchased was 130, the objective is to determine the cost of each item. This article will guide you through the algebraic equations and steps involved to find the solution.
Defining Variables
Let the price of an exercise book be x. According to the problem statement, the price of a textbook is four times that of an exercise book, thereby the price of a textbook is 4x.
Setting Up Equations
The first step is to set up equations based on the information provided:
The total expenditure on textbooks is $25,000, which can be represented as 25,000 / 4x, resulting in 6250 / x. This is the number of textbooks purchased. The total expenditure on exercise books is $10,000, equivalent to 10,000 / x, which is the number of exercise books purchased. According to the problem, the total number of items purchased is 130, resulting in the equation (6250 / x) (10,000 / x) 130.Solving the Equation
The combined equation is simplified as follows:
(6250 10,000) / x 130
This simplifies to 16250 / x 130
To solve for x, multiply both sides by x and divide by 130:
16250 13 > x 16250 / 130 > x 125
The cost of an exercise book is determined to be $125.
Now, to find the cost of a textbook, use the equation:
4x 4 × 125 $500
Therefore, the cost of a textbook is $500.
Summary of Costs
With the price of an exercise book as $125 and that of a textbook as $500, we can proceed to calculate the total cost of all items:
Number of textbooks: 25,000 / 500 50 Number of exercise books: 10,000 / 125 80The total cost of textbooks is: 50 × 500 $25,000
The total cost of exercise books is: 80 × 125 $10,000
Thus, the total cost of all items is 25,000 10,000 $35,000.
Conclusion
The total cost of the textbooks and exercise books is $35,000. This problem demonstrates the use of algebraic equations to solve real-world mathematical problems efficiently.