Question

A student's course grades and their corresponding weights are given in the table.

Category Grade Earned Weight by Category
Attendance 100% 10%
Tests 70% 30%
Homework 80% 20%
Final Exam 40%

What is the minimum grade needed on the final exam to earn an overall grade of 85% in the class?

Answer 1

Explanation:

Minimum grade needed: N/A

Default (GPT-3.5)

User

A student's course grades and their corresponding weights are given in the table.

Category Grade Earned Weight by Category

Attendance 100% 10%

Tests 70% 30%

Homework 80% 20%

Final Exam 40%

What is the minimum grade needed on the final exam to earn an overall grade of 85% in the class?

ChatGPT

To calculate the minimum grade needed on the final exam to earn an overall grade of 85%, we can use the weighted average formula. The weighted average is calculated by multiplying each grade earned by its corresponding weight and then summing up these values.

Let's break down the problem step by step:

First, calculate the weighted grade for each category:

Attendance: 100% * 10% = 10%

Tests: 70% * 30% = 21%

Homework: 80% * 20% = 16%

Final Exam: We'll denote this grade as "x" since we need to find it. Its weight is 40%.

Now, add up all the weighted grades:

Weighted Average = Attendance + Tests + Homework + Final Exam

Weighted Average = 10% + 21% + 16% + 40% = 87%

The student's current weighted average is 87%. To find the minimum grade needed on the final exam to earn an overall grade of 85%, we set up the equation:

Weighted Average = 85%

87% + 40% * x = 85%

Now, solve for "x" (the grade needed on the final exam):

40% * x = 85% - 87%

40% * x = -2%

x = (-2%) / 40%

x = -0.05

The calculated value for "x" is -0.05, which is negative. This implies that it is not possible to achieve an overall grade of 85% in the class, given the current grades and weights, because the weighted average is already higher than 85%. Double-checking the calculations, we find that the student's current weighted average is 87%, which is greater than the desired 85%.

It's worth noting that this means the student has already achieved an overall grade higher than the target grade of 85%, so no additional points are needed to meet the target.

Answer 2

Explanation:

To calculate the minimum grade needed on the final exam to earn an overall grade of 85%, we can use the concept of weighted averages. Weighted averages take into account both the grades earned and their corresponding weights.

Let's break down the steps to calculate the minimum grade needed on the final exam:

Step 1: Calculate the weighted grade for each category.

Attendance: Weighted grade = 100% * 10% = 10%

Tests: Weighted grade = 70% * 30% = 21%

Homework: Weighted grade = 80% * 20% = 16%

Final Exam: Weighted grade = Unknown (let's call it "X") * 40%

Step 2: Calculate the overall weighted grade.

Overall weighted grade = Sum of weighted grades for all categories

Overall weighted grade = 10% + 21% + 16% + (X * 40%)

Step 3: Set up the equation for the desired overall grade.

Since the desired overall grade is 85%, we can set up the following equation:

85% = Overall weighted grade

Step 4: Solve for X (the minimum grade needed on the final exam).

85% = 10% + 21% + 16% + (X * 40%)

Now, let's solve for X:

85% = 47% + (X * 40%)

Subtract 47% from both sides:

38% = X * 40%

Divide both sides by 40%:

X = 38% / 40%

X = 0.95

Step 5: Convert X to a percentage grade.

X represents the minimum grade needed on the final exam, so we need to convert it to a percentage grade:

Minimum grade needed on the final exam = 0.95 * 100% = 95%

Therefore, the student needs to score at least 95% on the final exam to earn an overall grade of 85% in the class.