Solving the Gift Price Puzzle: A Comprehensive SEO Guide
Have you ever been stumped by a seemingly complex puzzle involving the sharing of a gift price? This article, structured to meet Google's SEO standards, breaks down the problem into simple, understandable parts, using algebra to find the solution. Learn how to solve complex problems like this and master critical algebraic methods essential for problem-solving.
Let's explore a classic puzzle involving four friends—A, B, C, and D—buying a gift. Each friend contributes a specific fraction of the total price, creating a fascinating example of problem-solving. We will solve this problem step-by-step, ensuring it is accessible and SEO-friendly.
The Problem
Four friends A, B, C, and D bought a gift. A paid half of the price. B paid 1/3rd of what others paid. C paid 1/4th of what others paid. D paid Rs. 100. What is the price of the gift?
Step-by-Step Solution
Denoting the Total Price
Let's denote the total price of the gift as X.
Calculating Individual Contributions
Step 1: A paid half the price.
As A paid half the price, A's contribution is X/2.
Step 2: B paid 1/3rd of what others paid.
Others paid X - X/2 X/2. Therefore, B paid 1/3 of this, which is (X/2)/3 2X/9.
Step 3: C paid 1/4th of what others paid.
Others paid X - X/2 - 2X/9 3X/4. Therefore, C paid 1/4 of this, which is (3X/4)/4 3X/16.
Step 4: D paid Rs. 100.
D's contribution is given as 100.
Summing Up Contributions
Total contribution A's contribution B's contribution C's contribution D's contribution.
Total contribution X/2 2X/9 3X/16 100.
Let's solve this equation:
Total contribution X/2 2X/9 3X/16 10016X/16 36X/144 27X/144 2400/16 X79X/144 150 X79X/144 X - 15079X 144X - 2160065X 2160 333.33
Therefore, the price of the gift is Rs. 333.33.
Alternative Solution
We can also denote the contributions of A, B, C, and D as a, b, c, and d respectively.
Step 5: B pays 1/3rd of what others are paying.
The others pay 3b. Therefore, the total is 4b.
Step 6: A pays 1/2 of what others are paying.
A pays a and the others pay 2a. So the total is 3a which must be equal to 4b. Hence, 3a 4b or a 4/3b.
Step 7: C pays 1/4th of what others are paying.
The others pay 4c. Therefore, the total is 5c which must be equal to 4b. Hence, 5c 4b or c 4/5b.
Step 8: acd 3b.
Substituting the values of a and c, we get:
4/3b * 4/5b * d 3b d * 16/15b 3b d 13/15b b 15 d 13D pays Rs. 13.
Final Analysis
Using these steps, we can see that the price of the gift is Rs. 333.33, and D paid Rs. 13.
Conclusion
This puzzle not only tests your algebraic skills but also demonstrates the importance of step-by-step problem-solving. The key is to break down the problem into manageable parts and use algebra to find the solution.
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