Jane is taking a class and asks you to help her figure out what her last grade must be in the class to get a 85 in the class. She tells you the following calculation is used to find your final grade:
w2d2
x is her last score which has not been taken. Explain this equation and the process you would use to solve for the unknown test score. Solve for the test score.
Online "^" is used to indicate an exponent, e.g., x^2 = x squared.
I have no idea what w and d stand for to construct the equation.
The expression "w2d2" represents the weighted average of Jane's scores in the class. Each score is multiplied by a weight factor represented by 'w' and the position of the score in the calculation is represented by 'd'.
To solve for Jane's unknown test score, we need to know the specific weights assigned to each score and at which position the unknown score will be placed in the calculation. It seems 'w2d2' implies that Jane's final grade is calculated as follows:
Final grade = (w1 × s1) + (w2 × s2) + ... + (w × s) + (x × w2)
Where:
- 's1', 's2', ..., 's' are the known scores Jane has already received,
- 'w1', 'w2', ..., 'w' are the weights assigned to each respective score, and
- 'x' is the unknown test score.
To solve for the test score, you should follow these steps:
1. Assign numerical values to the known scores and their respective weights.
2. Determine the position ('d') of the unknown test score in the calculation. If Jane has only one test remaining and it will be the last score factored in, then 'd2' would mean it is in the second position (the final score).
3. Plug in the values into the equation.
4. Rearrange the equation to solve for 'x', the unknown test score.
5. Calculate the value of 'x' using algebraic manipulation.
For example, let's say Jane has received two scores so far: a score of 90 with a weight of 0.6 (w1 = 0.6, s1 = 90) and a score of 80 with a weight of 0.4 (w2 = 0.4, s2 = 80). If her unknown test score will be the final score (d2), we can set up the equation as:
85 = (0.6 × 90) + (0.4 × 80) + (x × 0.4)
To solve for 'x' (the unknown test score), we can rearrange the equation as follows:
85 - (0.6 × 90) - (0.4 × 80) = x × 0.4
Now we can calculate the value of 'x' by dividing both sides of the equation by 0.4:
x = (85 - (0.6 × 90) - (0.4 × 80)) / 0.4
By performing the calculations, we will find the value of 'x', which represents the test score Jane needs to get in order to achieve an 85 in the class.