To determine Libby's score, we need to find the total number of questions and the number of questions she answered correctly.

Let's denote the total number of questions as "n". Since each question is worth the same amount of points, we can find the value of each question by dividing the total possible score by the total number of questions:

Points per question = Total possible score / Total number of questions

Points per question = 800 / n

Now, we know that Libby misses 3% of the questions. To find the number of questions she answered correctly, we can first determine how many questions she missed:

Number of missed questions = 0.03 * n

Since she missed these questions, the number of questions she answered correctly is:

Number of correct questions = n - (0.03 * n)

Number of correct questions = n * (1 - 0.03)

Number of correct questions = 0.97 * n

To find her score, we multiply the number of correct questions by the points per question:

Libby's score = Number of correct questions * Points per question

Libby's score = (0.97 * n) * (800 / n)

The "n" terms cancel each other out:

Libby's score = 0.97 * 800

Now, calculate the result:

Libby's score = 776

So, Libby scores 776 points out of a total possible score of 800.