College

Brynn's quiz grades on her first four quizzes were 92, 97, 83, and 89. What score on the last quiz will allow her to finish with an average of at least 90?

A. [tex]x \geq 90[/tex]

B. [tex]x \leq 89[/tex]

C. [tex]x \textgreater 89[/tex]

D. [tex]x \geq 89[/tex]

Answer :

To find out what score Brynn needs on the last quiz to have an average of at least 90, we can follow these steps:

1. Calculate the Total Number of Quizzes: Brynn will take a total of 5 quizzes since she has already taken 4 and will take 1 more.

2. Calculate the Desired Total Score: We want Brynn's average score to be at least 90 over all 5 quizzes. To find the total score needed to achieve this average, we multiply the desired average by the total number of quizzes:

[tex]\[
\text{Total score needed} = 90 \times 5 = 450
\][/tex]

3. Calculate the Current Total Score: Add up the scores from the first four quizzes:

[tex]\[
92 + 97 + 83 + 89 = 361
\][/tex]

4. Determine the Score Needed on the Last Quiz: Subtract the current total score from the total score needed:

[tex]\[
\text{Score needed on the last quiz} = 450 - 361 = 89
\][/tex]

Based on the calculated score needed, Brynn needs at least an 89 on her last quiz to have an average of 90. Therefore, the correct option is:

(D) [tex]\( x \geq 89 \)[/tex]

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