How to Solve a Cricket Scoring Puzzle Using Algebra
Introduction to the Problem
Cricket, a popular sport worldwide, often involves complex mathematical puzzles that challenge even the most seasoned fans. In this article, we will explore a specific problem related to the batting averages of a cricket player. The logic behind solving such problems not only sharpens our analytical skills but also provides a deeper understanding of the sport. Let's dive into the details of the problem and the step-by-step solution.
The Problem: Batting Average Calculation
The batting average for 40 innings of a cricket player is 50 runs. His highest score exceeds his lowest score by 172 runs. If these two innings are excluded, the average of the remaining 38 innings is 48 runs. The question is: What is the highest score of the player?
Step-by-Step Solution
Let's break down the problem using algebra. Here are the steps to solve it:
1. Calculate the Total Runs Scored in 40 Innings
Given the average for 40 innings:
N 40
Average 50 runs
Total runs N * Average 40 * 50 2000 runs
2. Calculate the Total Runs Scored in the Remaining 38 Innings
Given the average for the remaining 38 innings:
N' 38
Average' 48 runs
Total runs for 38 innings N' * Average' 38 * 48 1824 runs
3. Calculate the Total Runs Scored in the Two Excluded Innings
Total runs for the two excluded innings Total runs for 40 innings - Total runs for 38 innings
2000 - 1824 176 runs
4. Set Up the Equations for the Highest and Lowest Scores
Let the lowest score be L and the highest score be H. We know that:
H - L 172
L H 176
5. Solve the Equations
From the first equation:
H L 172
Substitute H in the second equation:
L (L 172) 176
2L 172 176
2L 176 - 172
2L 4
L 2
Substitute L back to find H:
H L 172 2 172 174
Conclusion
The highest score of the player is 174 runs. This solution not only provides the answer but also demonstrates the application of algebra in solving real-world cricket problems.
Related Topics and Keywords
Cricket Scoring Puzzle: A mathematical problem related to cricket that challenges the player's analytical skills.
Average Runs: The mean value of runs scored in cricket over a specific period or innings.
Highest and Lowest Score Calculation: The technique of finding the highest and lowest scores in a set of cricket innings given the average and certain conditions.