Achieving an Average: Calculating Scores for Frederica's Test
In this article, we will delve into the process of determining the necessary score for a student, Frederica (often simplified as Freda), to achieve a specific average score in her tests. This involves using both a straightforward approach and a more formal mathematical method. Let's explore the steps to find the score required in the fourth test to achieve an average of 85.
Inspection Method
Firstly, we will use the inspection method, which involves some logical reasoning without extensive calculation. Freda has already taken three tests with scores of 82, 74, and 90. We need to find out what score she must achieve on her fourth test to reach an average of 85.
Given that the average score of 85 requires a total of 85 * 4 340 points across four tests, we can determine the total score needed from the first three tests. The sum of 82, 74, and 90 is 246. Therefore, the score required in the fourth test, denoted as x, can be found by solving the equation:
246 x 340
Solving for x:
x 340 - 246 94
By inspection, we can see that adding 9 to each of the first three scores would get us to 85. Therefore, Freda needs to score 94 in her fourth test to achieve an average of 85.
More Formal Method
For a more formal approach, we can use the formula for the average score:
Average Score Total of all scores / Number of tests
Let x be the score Freda needs on her fourth test. The average required is 85, and she needs to take four tests. The total score required for an average of 85 is:
Average Total / Number of tests
85 (82 74 90 x) / 4
Multiplying both sides by 4 to clear the denominator:
340 246 x
Solving for x:
x 340 - 246 94
Thus, the more formal calculation also confirms that Freda needs to score 94 in her fourth test to achieve an average of 85.
Conclusion
Whether through inspection or formal calculation, both methods lead to the same conclusion. Freda needs to score 94 on her fourth test to achieve an average of 85. This method can be applied to any similar problem where you need to determine the required score to achieve a specific average.