Answer :
To determine what score Brynn needs on her last quiz to achieve an average of at least 90, follow these steps:
1. Understand the problem: Brynn has taken four quizzes, and her scores are 92, 97, 83, and 89. She wants the average of these four scores plus a fifth score (let's call it [tex]\( x \)[/tex]) to be at least 90.
2. Set up the equation for the average: The average score needed is 90. So, the equation is:
[tex]\[
\frac{92 + 97 + 83 + 89 + x}{5} \geq 90
\][/tex]
3. Calculate the total of the current scores: Add up the scores of the first four quizzes.
[tex]\[
92 + 97 + 83 + 89 = 361
\][/tex]
4. Set up the inequality for the total score needed:
Multiply the desired average (90) by the number of quizzes (5) to find the total score Brynn needs from all five quizzes.
[tex]\[
5 \times 90 = 450
\][/tex]
5. Determine the score needed on the last quiz: You need the sum of all quiz scores to be at least 450 to achieve the desired average.
[tex]\[
361 + x \geq 450
\][/tex]
6. Solve for [tex]\( x \)[/tex]:
Subtract 361 from 450 to find the minimum score needed on the last quiz.
[tex]\[
x \geq 450 - 361
\][/tex]
[tex]\[
x \geq 89
\][/tex]
7. Conclusion: Brynn needs to score at least 89 on her last quiz to have an average of at least 90.
So, the correct answer is option (D) [tex]\( x \geq 89 \)[/tex].
1. Understand the problem: Brynn has taken four quizzes, and her scores are 92, 97, 83, and 89. She wants the average of these four scores plus a fifth score (let's call it [tex]\( x \)[/tex]) to be at least 90.
2. Set up the equation for the average: The average score needed is 90. So, the equation is:
[tex]\[
\frac{92 + 97 + 83 + 89 + x}{5} \geq 90
\][/tex]
3. Calculate the total of the current scores: Add up the scores of the first four quizzes.
[tex]\[
92 + 97 + 83 + 89 = 361
\][/tex]
4. Set up the inequality for the total score needed:
Multiply the desired average (90) by the number of quizzes (5) to find the total score Brynn needs from all five quizzes.
[tex]\[
5 \times 90 = 450
\][/tex]
5. Determine the score needed on the last quiz: You need the sum of all quiz scores to be at least 450 to achieve the desired average.
[tex]\[
361 + x \geq 450
\][/tex]
6. Solve for [tex]\( x \)[/tex]:
Subtract 361 from 450 to find the minimum score needed on the last quiz.
[tex]\[
x \geq 450 - 361
\][/tex]
[tex]\[
x \geq 89
\][/tex]
7. Conclusion: Brynn needs to score at least 89 on her last quiz to have an average of at least 90.
So, the correct answer is option (D) [tex]\( x \geq 89 \)[/tex].
