Solving Mathematical Word Problems: A Dictionary Costs Three Times as Much as a Story Book

Mathematics often requires us to translate real-world scenarios into algebraic expressions to solve for unknown quantities. This tutorial shows you how to solve the mathematical word problem: 'A dictionary costs three times as much as a story book. If the total cost of one dictionary and one story book is $600, what is the price of the story book?'

Simplified Approach to Solving the Problem

Let's denote the cost of the story book as x. Consequently, the cost of the dictionary will be 3x, as it is three times the cost of the story book.

Step 1: Setting Up Equations

Given that the total cost of one dictionary and one story book is $600, we can create the following equation:

Cost of the story book: x Cost of the dictionary: 3x Total cost: x 3x 4x

The equation becomes:

4x 600

Step 2: Solving for x

To find the value of ( x ), we need to divide both sides of the equation by 4:

x 600 / 4

x 150

Therefore, the cost of the story book is $150.

Step-by-Step Breakdown Solutions

Solution 1

Let the cost of the story book be x. Then, the cost of the dictionary is 3x. The total cost is given as $600, so we can set up the following equation:

x 3x 600

Simplifying the left side, we get:

4x 600

Dividing both sides by 4:

x 600 / 4

x 150

The cost of the story book is $150.

Solution 2

Let x denote the cost of the story book. Therefore, the cost of the dictionary is 3x. According to the given information:

x 3x 600

This simplifies to:

4x 600

To solve for x, divide both sides by 4:

x 600 / 4

x 150

Therefore, the cost of the story book is $150.

Solution 3

Let x be the cost of one book. According to the problem, a dictionary costs 3x. The total cost of one dictionary and one story book is $600, so:

x 3x 600

Simplifying the equation:

4x 600

Dividing both sides by 4:

x 600 / 4

x 150

Hence, the price of the book is $150.

The same logic applies to the other provided solutions which lead to the same conclusion.

Conclusion

Through this series of algebraic manipulations, we have demonstrated that the cost of the story book is $150. This problem is a straightforward example of setting up and solving linear equations. Understanding these techniques is crucial for solving more complex mathematical problems in the future.