Question

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.

• A. $66\le y\le 93$
• B. $66\le y\le 100$
• C. $80\le y\le 89$
• D. $80\le y\le 93$

Answer 1

The correct option is A $66\le y\le 93$

Given, in Roscher's class a student with an average score $80$ to $89$, gets a $B$ grade in based $3$ tests.

Roscher scored $79$ points in his first test and $95$ in second test and he get y scored in third test.

Then $79+95+y=y+174$ are total marks scored Roscher in all tests.

If the average score is $80$

Then $y+174=3\times 80$

$\Rightarrow y+174=240$

$\Rightarrow y=240-174=66$

If the average score is $80$

Then $y+174=3\times 89$

$\Rightarrow y+174=267$

$\Rightarrow y=267-174=93$

Then inequalities is $66\le y\le 93$