Matt scored 75 on the calculus midterm. If the final exam counts twice as much as the midterm exam, then for wht range of scores on the final would Matt get an average between 81 and 92?
average=(75+2*FE)/3
solve for FE given average is 81, then 92
another way to look at it: if he wants an 81, and is already 6 point behind that, then he needs 3 points on the FE above 81 to score that average.
scored 56, needs between 76 and 87
To find the range of scores on the final exam for which Matt would get an average between 81 and 92, we can set up an equation:
Let's assume Matt's score on the final exam is 'x'.
The average is calculated by taking the sum of all the scores and dividing by the total number of scores.
The total score for Matt will be the sum of his midterm score (75) and twice the final exam score (2x).
Now, let's set up the equation:
(75 + 2x) / 3 = (81 + 92) / 2
To solve for x, we need to isolate it.
Multiply both sides of the equation by 3:
75 + 2x = (81 + 92) * 3 / 2
Simplify:
75 + 2x = 173.25
Subtract 75 from both sides:
2x = 173.25 - 75
2x = 98.25
Divide both sides by 2:
x = 98.25 / 2
x = 49.125
Therefore, for Matt to get an average between 81 and 92, his score on the final exam should be between 49.125 (inclusive) and any higher value.
To find the range of scores on the final exam that would result in an average between 81 and 92, we need to set up an equation.
Let's denote the score on the final exam as "f." Since the final exam counts twice as much as the midterm exam, we can consider it as having a weight of 2. Thus, the total score for Matt's grade would be:
Total score = Midterm score + 2 * Final score
We know the midterm score is 75, so the total score becomes:
Total score = 75 + 2 * Final score
To find the range of scores on the final exam that would yield an average between 81 and 92, we can set up the following inequality:
((Total score) + 75) / 3) >= 81
((Total score) + 75) / 3) <= 92
Let's simplify these equations:
81 <= ((75 + 2 * Final score) / 3) <= 92
Now we can solve the inequality. First, multiply both sides of the inequality by 3:
243 <= 75 + 2 * Final score <= 276
Next, subtract 75 from all parts of the inequality:
243 - 75 <= 75 + 2 * Final score - 75 <= 276 - 75
168 <= 2 * Final score <= 201
Divide all parts of the inequality by 2:
84 <= Final score <= 100.5
Therefore, the range of scores on the final exam for Matt to achieve an average between 81 and 92 is 84 to 100.5 (inclusive).