Problem 74 - Elementary Algebra Within Reach

Question

Quiz Grade In your statistics class, there are eight 20-point quizzes. To earn an A for the quizces, you must have a total of at least \(90 \%\) of the points. On the first 7 quizzes, your scores were \(19,20,20,15,19,14\), and 18 . How many points do you have to obtain on the eighth quiz in order to earn an A for the quizzes?

Step-by-Step Solution

Answer

To earn an A grade in the quizzes, you must score at least 19 points on the eighth quiz.

Step 1: Calculate the total points on the first 7 quizzes

Firstly, sum up the points earned from the first seven quizzes. The scores obtained were \(19,20,20,15,19,14\), and \(18\). By summation, the total score from the first seven quizzes is \(19 + 20 + 20 + 15 + 19 + 14 + 18 = 125\) points.

Step 2: Calculate the needed score for the last quiz

Secondly, find the required points for the eighth quiz. The total points required to achieve 'A' grade is \(144\) points (as calculated in the analysis). Subtract the total points already earned (which is \(125\)) from the target total \(144\). As such, the points needed on the last quiz is \(144 - 125 = 19\) points.

Key Concepts

Quiz Score Calculation

When calculating quiz scores, it's crucial to understand the value of each quiz and the total possible points. In the given exercise, we have eight quizzes, each worth 20 points. The first step to any calculation is gathering the scores obtained on each quiz. For this example:

• First quiz: 19 points
• Second quiz: 20 points
• Third quiz: 20 points
• Fourth quiz: 15 points
• Fifth quiz: 19 points
• Sixth quiz: 14 points
• Seventh quiz: 18 points

To find the total score so far, simply add these scores together. Adding them gives us a subtotal, which is a crucial step in understanding how much more you need to score.

Percentage Requirement

The percentage requirement acts as a benchmark to achieve a particular grade. In this exercise, an A grade requires at least 90% of the total available points for the quizzes. Each quiz is worth 20 points, and with eight quizzes, the total points possible are:\[8 \times 20 = 160\]To find out how many points represent 90% of 160, we need to calculate:\[160 \times 0.9 = 144\]This means that to secure an A grade, a student must score at least 144 points out of the total 160 available points. Understanding this requirement can guide students in tracking their progress and focus their efforts accordingly.

Summation of Scores

Summing up scores correctly is the key to knowing your current standing. From the scores listed in the given exercise:- First quiz: 19 points- Second quiz: 20 points- Third quiz: 20 points- Fourth quiz: 15 points- Fifth quiz: 19 points- Sixth quiz: 14 points- Seventh quiz: 18 pointsAdding these scores results in:\[19 + 20 + 20 + 15 + 19 + 14 + 18 = 125\]This subtotal, 125, is the foundation for calculating how much is further needed from the remaining quiz or quizzes to meet the percentage requirement. Always ensure accuracy in your addition since this sum forms the base of all subsequent calculations.

Grade Requirement Calculation

With a clear understanding of the percentage requirement and the sum of the scores so far, we can calculate what's needed on the remaining quizzes. From the earlier calculations, we know:- Total 'A' grade requirement is 144 points- Current total score is 125 pointsTo find out how many points are needed on the eighth quiz to reach 144 points, perform the following:\[144 - 125 = 19\]In addition, if the total score needed is greater than the maximum score of the last quiz, reevaluate your approach in earlier quizzes. In our case, 19 points are needed to reach the goal, which is feasible since each quiz has a maximum of 20 points. This understanding allows students to effectively strategize and prioritize their studying efforts on future assessments.