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 80% 30%
Homework 95% 20%
Final Exam 40%

What is the minimum grade needed on the final exam to earn an overall grade of 83% in the class?
30%
57%
75%
90%

Answer 1

To find the minimum grade needed on the final exam to achieve an overall grade of 83% in the class, we can set up the equation using the weights of each category.

### Step 1: Convert the weights to decimals
- Attendance: 10% = 0.10
- Tests: 30% = 0.30
- Homework: 20% = 0.20
- Final Exam: 40% = 0.40

### Step 2: Set up the equation
Let \( x \) be the grade needed on the final exam. The overall grade can be calculated using the formula:

\[
\text{Overall Grade} = (\text{Attendance Grade} \times \text{Weight}) + (\text{Test Grade} \times \text{Weight}) + (\text{Homework Grade} \times \text{Weight}) + (x \times \text{Weight})
\]

Substituting the known values into the equation:

\[
0.10 \times 100 + 0.30 \times 80 + 0.20 \times 95 + 0.40 \times x = 83
\]

### Step 3: Calculate the contributions of each category
- Attendance contribution: \( 0.10 \times 100 = 10 \)
- Tests contribution: \( 0.30 \times 80 = 24 \)
- Homework contribution: \( 0.20 \times 95 = 19 \)

### Step 4: Combine the contributions and solve for \( x \)
Now plug these values back into the equation:

\[
10 + 24 + 19 + 0.40x = 83
\]

Combine the known contributions:

\[
53 + 0.40x = 83
\]

Subtract 53 from both sides:

\[
0.40x = 30
\]

### Step 5: Solve for \( x \)
Now, divide both sides by 0.40:

\[
x = \frac{30}{0.40} = 75
\]

### Conclusion
The minimum grade needed on the final exam to earn an overall grade of 83% in the class is **75%**. Thus, the answer is:

**75%**