Jayne is taking two AP classes and three regular classes. Her AP classes count twice as much as her regular classes in her GPA. Each grade has the following point value: A = 4 points, B = 3 points, C = 2 points, D = 1 point.
What is Jayne's GPA?
| Class | Jayne's grade | |---------------|---------------| | AP English | C | | AP Government | B | | Algebra II | B | | Spanish | D | | Physics | A |
### Step 1: Assign Grade Points Let's assign the grade points as follows: - A = 4 points - B = 3 points - C = 2 points - D = 1 point
### Step 2: Weights of Classes Jayne's AP classes count twice as much as her regular classes: - AP class weight = 2 - Regular class weight = 1
### Step 3: List Classes and Grades Jayne's grades are: - AP English: C - AP Government: B - Algebra II: B - Spanish: D - Physics: A
### Step 4: Convert Grades to Points Next, convert the grades into their respective points: - AP English: C = 2 points - AP Government: B = 3 points - Algebra II: B = 3 points - Spanish: D = 1 point - Physics: A = 4 points
### Step 5: Calculate Weighted Points Now, apply the weights to each class and sum the total points and total weights. - AP English: [tex]\(2 \text{ points} \times 2 \text{ (AP weight)} = 4 \text{ weighted points}\)[/tex] - AP Government: [tex]\(3 \text{ points} \times 2 \text{ (AP weight)} = 6 \text{ weighted points}\)[/tex] - Algebra II: [tex]\(3 \text{ points} \times 1 \text{ (regular weight)} = 3 \text{ weighted points}\)[/tex] - Spanish: [tex]\(1 \text{ point} \times 1 \text{ (regular weight)} = 1 \text{ weighted point}\)[/tex] - Physics: [tex]\(4 \text{ points} \times 1 \text{ (regular weight)} = 4 \text{ weighted points}\)[/tex]
Now, we can calculate: - Total Points = [tex]\(4 + 6 + 3 + 1 + 4 = 18\)[/tex] - Total Weight = [tex]\(2 + 2 + 1 + 1 + 1 = 7\)[/tex]
### Step 6: Calculate GPA Finally, calculate the GPA by dividing the total weighted points by the total weight: [tex]\[ \text{GPA} = \frac{\text{Total Weighted Points}}{\text{Total Weight}} = \frac{18}{7} \approx 2.571 \][/tex]
