Answer :
First, note that Cora is enrolled in three AP classes and two regular classes. The AP classes have double the weight of the regular classes in calculating the GPA.
The grades have the following point values:
- [tex]\( A = 4 \)[/tex] points
- [tex]\( B = 3 \)[/tex] points
Cora's classes and corresponding grades are:
- AP classes: AP English, AP Government, AP Algebra II, each with an [tex]\( A \)[/tex] (worth [tex]\(4\)[/tex] points)
- Regular classes: Spanish with a [tex]\( B \)[/tex] (worth [tex]\(3\)[/tex] points) and Physics with an [tex]\( A \)[/tex] (worth [tex]\(4\)[/tex] points)
Step 1. Calculate the weighted points for the AP classes.
For the three AP classes:
[tex]\[
\text{Total points from AP classes} = 4 + 4 + 4 = 12
\][/tex]
Since each AP class counts twice as much:
[tex]\[
\text{Weighted points from AP classes} = 12 \times 2 = 24
\][/tex]
Step 2. Calculate the weighted points for the regular classes.
For the two regular classes:
[tex]\[
\text{Total points from regular classes} = 3 + 4 = 7
\][/tex]
Each regular class has a weight of 1, so:
[tex]\[
\text{Weighted points from regular classes} = 7 \times 1 = 7
\][/tex]
Step 3. Compute the total weighted points.
[tex]\[
\text{Total weighted points} = 24 + 7 = 31
\][/tex]
Step 4. Determine the total weight.
For the AP classes (with double weight):
[tex]\[
\text{Total weight for AP classes} = 3 \times 2 = 6
\][/tex]
For the regular classes:
[tex]\[
\text{Total weight for regular classes} = 2 \times 1 = 2
\][/tex]
Thus, the total weight is:
[tex]\[
\text{Total weight} = 6 + 2 = 8
\][/tex]
Step 5. Calculate the GPA.
The GPA is given by the total weighted points divided by the total weight:
[tex]\[
\text{GPA} = \frac{31}{8} \approx 3.875
\][/tex]
When rounded to one decimal place, the GPA is:
[tex]\[
\boxed{3.9}
\][/tex]
Thus, Cora's GPA is [tex]\(3.9\)[/tex].
The grades have the following point values:
- [tex]\( A = 4 \)[/tex] points
- [tex]\( B = 3 \)[/tex] points
Cora's classes and corresponding grades are:
- AP classes: AP English, AP Government, AP Algebra II, each with an [tex]\( A \)[/tex] (worth [tex]\(4\)[/tex] points)
- Regular classes: Spanish with a [tex]\( B \)[/tex] (worth [tex]\(3\)[/tex] points) and Physics with an [tex]\( A \)[/tex] (worth [tex]\(4\)[/tex] points)
Step 1. Calculate the weighted points for the AP classes.
For the three AP classes:
[tex]\[
\text{Total points from AP classes} = 4 + 4 + 4 = 12
\][/tex]
Since each AP class counts twice as much:
[tex]\[
\text{Weighted points from AP classes} = 12 \times 2 = 24
\][/tex]
Step 2. Calculate the weighted points for the regular classes.
For the two regular classes:
[tex]\[
\text{Total points from regular classes} = 3 + 4 = 7
\][/tex]
Each regular class has a weight of 1, so:
[tex]\[
\text{Weighted points from regular classes} = 7 \times 1 = 7
\][/tex]
Step 3. Compute the total weighted points.
[tex]\[
\text{Total weighted points} = 24 + 7 = 31
\][/tex]
Step 4. Determine the total weight.
For the AP classes (with double weight):
[tex]\[
\text{Total weight for AP classes} = 3 \times 2 = 6
\][/tex]
For the regular classes:
[tex]\[
\text{Total weight for regular classes} = 2 \times 1 = 2
\][/tex]
Thus, the total weight is:
[tex]\[
\text{Total weight} = 6 + 2 = 8
\][/tex]
Step 5. Calculate the GPA.
The GPA is given by the total weighted points divided by the total weight:
[tex]\[
\text{GPA} = \frac{31}{8} \approx 3.875
\][/tex]
When rounded to one decimal place, the GPA is:
[tex]\[
\boxed{3.9}
\][/tex]
Thus, Cora's GPA is [tex]\(3.9\)[/tex].
