Solving Keith's Baseball Trading Card Collection Problem: An SEO-Optimized Guide

In this article, we will dive into a fun and challenging puzzle involving Keith's baseball trading card collection. We'll explore the logical steps and mathematical equations to solve this problem, making it SEO-friendly and rich with useful keywords.

The Problem Statement and Initial Assumptions

Keith initially had a certain number of baseball trading cards in his collection. He then added 5 new cards. The following day, his dog ate half of his collection, leaving only 25 cards. The goal is to determine how many cards Keith originally had in his collection.

Logical Solution: Step-by-Step Analysis

Let's denote the number of baseball trading cards Keith originally had as x.

After adding 5 new cards, Keith had x 5 next day, his dog ate half of his collection leaving him with 25 can be represented by the equation:

frac{x 5}{2} 25

Mathematical Solution: Solving the Equation

To solve for x, we follow these steps:

Multiply both sides of the equation by 2:x 5 50Subtract 5 from both sides:x 45

Therefore, Keith originally had 45 baseball trading cards.

Verification and Conclusion

Let's verify the solution:

Keith had 45 cards.He bought 5 more, bringing the total to 50 cards.His dog ate half of the collection, leaving 25 cards.

This solution checks out, confirming that Keith started with 45 cards.

Additional Solutions and Analysis

Let's also consider the alternative solutions presented in the problem statements:

Solution 1: Number of cards at the start be X, number of cards after adding 8 new cards X 8, number of cards after 1/2 of them eaten by dog X 8 - (X 8)/2 46 → X 8 - 46 0 → X 38Solution 2: Let having z cards in the first, after add cards z 8, next day card will be (z 8) - (z 8)/2 (z 8)/2, given (z 8)/2 46 → z 92 - 8 84, start with 84 cardsSolution 3: X number of cards he started with, X 8/2 46, X 8 92, X 84 cards were at the start

These solutions involve variations in the number of cards Keith added and the assumption of different operations. However, the consistent logical and mathematical approach leads us to the same conclusion: Keith started with 45 cards.

SEO Optimization and Keywords

To ensure high SEO performance, we have included the following keywords in our content:

baseball trading cards: This keyword is frequently searched in the context of collecting and trading.collection problem: This keyword helps target those interested in solving logical puzzles and mathematical problems.: This keyword caters to users seeking logical and mathematical content.