Math Puzzles: How Much Did Cindy and Dino Spend?

Welcome to today's dive into a fun and challenging math puzzle that has been making rounds online. This problem involves basic algebra and logical reasoning, making it a great tool for enhancing problem-solving skills. Let's explore the math problem faced by Cindy and Dino, and break down how to solve it step-by-step.

Understanding the Problem

The scenario involves Cindy and Dino, with the initial conditions as follows: Cindy has 1/3 as much money as Dino. After each spends an equal amount, Cindy has Rs. 100 left, while Dino has 3/4 of his original amount left. We need to determine how much each one spent.

Solving the Puzzle

Step-by-Step Solution

Let's denote Dino's initial amount as D rupees, and Cindy's initial amount as C rupees. According to the problem, Cindy has 1/3 of Dino's money, so we can write:

C D/3

Let's denote the amount each spent as x rupees. After spending, Cindy has 100 rupees left, and Dino has 3/4 of his original amount left, so we can write:

C - x 100

D - x (3/4)D

From the second equation, we can express x in terms of D:

x D - (3/4)D (1/4)D

Substituting x (1/4)D into the first equation:

C - (1/4)D 100

Since C D/3, substitute C in the equation:

D/3 - (1/4)D 100

Combine the terms on the left side:

(4D - 3D)/12 100

D/12 100

D 1200

Now that we have Dino's initial amount, we can find Cindy's initial amount:

C D/3 1200/3 400

Finally, we can find the amount each spent:

x (1/4)D (1/4)1200 300

So, each of them spent Rs. 300.

Verification

Let's verify the solution:

Cindy initially had Rs. 400, and after spending Rs. 300, she has Rs. 100 left.

Dino initially had Rs. 1200, and after spending Rs. 300, he has Rs. 900 left, which is 3/4 of his original amount.

Conclusion

The puzzle is complete, and we've determined that Cindy and Dino each spent Rs. 300. This problem not only tests your algebraic skills but also your logical reasoning ability. Whether you're a student looking to sharpen your math skills or a puzzle enthusiast, this problem is a great exercise.

Related Keywords

By incorporating these keywords into your content, you can enhance the visibility and relevance of your webpage to a wider audience, especially those interested in math and problem-solving.