Question

eden needs an average of 92% on her quiz scores to earn the grade she wants in science class. each quiz is worth 20 points. the scores of her first four quizzes are shown in the table.
quiz | score
1 | 20
2 | 18
3 | 19
4 | 17
there will be one more quiz. what is the minimum score she can receive to earn at least a 92% average on her science class quizzes?
a minimum score of 90 points

Explanation:

Step1: Calculate total points needed

To have an average of 92% over 5 quizzes (4 done, 1 more), first find total points needed. Each quiz is 20 points, so 92% of 20 per quiz. For 5 quizzes: $0.92\times20\times5 = 92$ points total.

Step2: Calculate total of first four quizzes

Sum the first four scores: $20 + 18 + 19 + 17 = 74$ points.

Step3: Find the minimum score for the fifth quiz

Subtract total of first four from total needed: $92 - 74 = 18$? Wait, no, wait. Wait, 92% of 20 is $0.92\times20 = 18.4$ points per quiz? Wait, no, the average is 92% of the total possible points? Wait, each quiz is 20 points, so 5 quizzes have total possible points $20\times5 = 100$ points? Wait, no, 20 points per quiz, 5 quizzes: total possible is $20\times5 = 100$ points. 92% of 100 is 92 points. So total points needed is 92.

First four quizzes: 20 + 18 + 19 + 17 = 74. So fifth quiz needs $92 - 74 = 18$? Wait, but 18 is 90% of 20? Wait, no, maybe I messed up. Wait, 92% average: average score per quiz is 92% of 20, which is $0.92\times20 = 18.4$ per quiz. For 5 quizzes, total score is $18.4\times5 = 92$ points. First four scores: 20 + 18 + 19 + 17 = 74. So fifth score: $92 - 74 = 18$? But 18 is 90% of 20, but wait, maybe the average is based on percentage of each quiz's score. Wait, each quiz is 20 points, so a score of x on a quiz is $\frac{x}{20}\times100\%$ percentage. So the average percentage is $\frac{\frac{20}{20}\times100 + \frac{18}{20}\times100 + \frac{19}{20}\times100 + \frac{17}{20}\times100 + \frac{s}{20}\times100}{5} \geq 92$.

Simplify: $\frac{100 + 90 + 95 + 85 + \frac{s}{20}\times100}{5} \geq 92$. Wait, no, $\frac{20 + 18 + 19 + 17 + s}{20\times5} \times100 \geq 92$. Let's compute numerator: total score is $20 + 18 + 19 + 17 + s = 74 + s$. Total possible is $100$ (20*5). So $\frac{74 + s}{100} \times100 \geq 92$ → $74 + s \geq 92$ → $s \geq 18$. Wait, but 18 is 90% of 20, but the average percentage would be $\frac{(100 + 90 + 95 + 85 + 90)}{5} = \frac{460}{5} = 92\%$. Ah, there we go. So the minimum score is 18? Wait, but the initial answer had 90, which is wrong. Wait, let's recalculate:

Total possible points for 5 quizzes: 20*5 = 100. 92% of 100 is 92 points.

First four quizzes: 20 + 18 + 19 + 17 = 74.

So fifth quiz needs 92 - 74 = 18 points. So the minimum score is 18. Wait, but maybe the question is about percentage of each quiz's score, but the calculation shows 18. Wait, maybe I made a mistake earlier. Let's check:

Quiz 1: 20/20 = 100%

Quiz 2: 18/20 = 90%

Quiz 3: 19/20 = 95%

Quiz 4: 17/20 = 85%

Quiz 5: x/20 = p%

Average percentage: (100 + 90 + 95 + 85 + p)/5 = 92

Sum of percentages: 100 + 90 + 95 + 85 = 370

So (370 + p)/5 = 92 → 370 + p = 460 → p = 90 → x = 0.9*20 = 18. So the minimum score is 18. Wait, but the initial input had "a minimum score of 90" which is wrong. So correct calculation:

Total points needed: 92% of (205) = 0.92100 = 92.

Total of first four: 20+18+19+17=74.

Fifth score: 92-74=18.

Answer:

18