Katie must take five exams in a math class. Her scores on the first four exams were 68, 66, 82, and 80. Answer the following questions:

The maximum score on an exam is 100 points. If it is not possible for Katie to achieve the required score on the exam, type np in the answer blank.

What is the minimum score must Katie get on the fifth exam for her overall mean to be at least 80? score = .

What is the minimum score must Katie get on the fifth exam for her overall mean to be at least 90? score

Mean = Sum of scores/number o f scores

80 ≤ (68 + 66 + 82 + 80 + x)/5

Solve for x.

Do the same for 90.

he got 459

To find the minimum score Katie must get on the fifth exam to achieve a certain overall mean, we can use the formula for calculating the mean.

The formula to calculate the mean is:
Mean = (sum of all scores) / (number of scores)

In this case, we have the scores of Katie's first four exams: 68, 66, 82, and 80.

To find the minimum score Katie must get on the fifth exam for her overall mean to be at least 80, we can set up the following equation:

(68 + 66 + 82 + 80 + score) / 5 ≥ 80

Let's solve this equation:

(296 + score) / 5 ≥ 80
Multiply both sides of the equation by 5:
296 + score ≥ 400
Subtract 296 from both sides of the equation:
score ≥ 400 - 296
score ≥ 104

Therefore, the minimum score Katie must get on the fifth exam for her overall mean to be at least 80 is 104.

Now, let's find the minimum score Katie must get on the fifth exam for her overall mean to be at least 90.

(296 + score) / 5 ≥ 90
Multiply both sides of the equation by 5:
296 + score ≥ 450
Subtract 296 from both sides of the equation:
score ≥ 450 - 296
score ≥ 154

Therefore, the minimum score Katie must get on the fifth exam for her overall mean to be at least 90 is 154.

I hope this helps! Let me know if you have any further questions.