Multiple choice

In Roscher's class, a student with an average score from $80$ to $89$, inclusive, gets a $B$ grade. His grade is based only on $3$ tests. The highest possible score on each of these tests is $100$ points. Roscher scored $79$ points in his first test and $95$ in his second test. If $y$ represents his score in the third test, determine which of the following inequalities below shows all values of $y$ that would earn Roscher a $B$ in his Physics class.

  1. $\displaystyle 66\le y\le 93$
  2. $\displaystyle 66\le y\le 100$
  3. $\displaystyle 80\le y\le 89$
  4. $\displaystyle 80\le y\le 93$
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Average score = (79 + 95 + y) / 3. For a B grade, 80 <= (174 + y) / 3 <= 89. 240 <= 174 + y <= 267. 66 <= y <= 93.

AI explanation

To earn a B grade, Roscher's average over the 3 tests must be between 80 and 89. We calculate the third test score, y, using the average formula. Multiplying the minimum required average of 80 by 3 tests gives a minimum total of 240 points, so 79 + 95 + y >= 240, which simplifies to y >= 66. Multiplying the maximum required average of 89 by 3 tests gives a maximum total of 267 points, so 79 + 95 + y <= 267, which simplifies to y <= 93. Therefore, the inequality representing the values of y that earn a B grade is 66 <= y <= 93.

Keep practicing — related questions