Solving a Word Problem: Finding the Cost of Roshan's Dictionary

In a stationary shop, Roshan spent Rs 180.50 on purchasing a dictionary, a pen, and a notebook. We are given that the dictionary costs twice as much as the pen and thrice as the notebook. How can we determine the price of the dictionary?

Let's break this down step by step to solve this intriguing problem.

Setting Up the Equations

Let the price of the dictionary be X. According to the problem:

The price of the dictionary X The price of the pen X / 2 The price of the notebook X / 3

We know the total cost is Rs 180.50, so we can write the equation:

Rs 180.50 X X/2 X/3

Combining the Terms

To combine the terms, we find a common denominator for the fractions. The common denominator for 2 and 3 is 6. Thus, the equation becomes:

180.50 6X/6 3X/6 2X/6

180.50 (6X 3X 2X) / 6

Solving the Equation

Combine the terms in the numerator:

180.50 (11X) / 6

To find X, we multiply both sides by 6:

180.50 × 6 11X

1083 11X

Now, divide both sides by 11:

X 1083 / 11

X 98.45

Conclusion

Therefore, the price of the dictionary is Rs 98.45. To break it down further:

The price of the dictionary Rs 98.45 The price of the pen 98.45 / 2 Rs 49.23 The price of the notebook 98.45 / 3 Rs 32.82

Thus, Roshan's expenditures are as follows:

Dictionary: Rs 98.45 Pen: Rs 49.23 Notebook: Rs 32.82

Adding these up, we indeed get Rs 180.50.

Google SEO Tips:

Use relevant keywords like "word problem," "algebra," and "equation solving" throughout your content. Make sure to include the exact solution and the steps taken to reach it. Add a conclusion that summarizes the findings to help search engines understand the content. Use subheadings for better readability and to organize the information logically.