Points to Remember:
- This is a mathematical word problem requiring an analytical approach.
- The problem involves calculating an average score based on a given increase after a specific inning.
- We need to use algebraic equations to solve for the unknown average.
Introduction:
This question is a classic example of a problem involving averages. Averages are crucial in various fields, from sports statistics to economic indicators. In this case, we are dealing with a batsman’s average runs scored per inning. The problem provides us with the score in the 15th inning and the resulting increase in the average, allowing us to determine the average after 15 innings. We will use algebraic methods to solve this problem.
Body:
1. Defining the Variables:
Let ‘x’ represent the batsman’s average score after 14 innings. The total runs scored in the first 14 innings would therefore be 14x.
2. Setting up the Equation:
After the 15th inning, the batsman’s total runs become 14x + 95. His new average is x + 5. The number of innings is now 15. Therefore, we can set up the following equation:
(14x + 95) / 15 = x + 5
3. Solving the Equation:
To solve for x, we follow these steps:
- Multiply both sides by 15: 14x + 95 = 15(x + 5)
- Expand the right side: 14x + 95 = 15x + 75
- Subtract 14x from both sides: 95 = x + 75
- Subtract 75 from both sides: x = 20
Therefore, the batsman’s average after 14 innings was 20 runs.
4. Calculating the Average After 15 Innings:
The average after 15 innings is x + 5, which is 20 + 5 = 25 runs.
Conclusion:
The batsman’s average after 15 innings is 25 runs. We arrived at this solution by setting up and solving an algebraic equation that represented the relationship between the total runs scored, the number of innings, and the average score. This problem highlights the importance of understanding averages and applying algebraic techniques to solve real-world problems. This analytical approach can be applied to various scenarios involving averages in different fields, promoting a better understanding of data analysis and interpretation. The ability to solve such problems fosters critical thinking and problem-solving skills, essential for holistic development.
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