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In one common system for finding a grade-point average, or GPA,

[tex]\[ A=4, B=3, C=2, D=1, F=0 \][/tex]

The GPA is calculated by multiplying the number of credit hours for a course by the number assigned to each grade, and then adding these products. Then divide this sum by the total number of credit hours. Because each course grade is weighted according to the number of credits of the course, GPA is called a weighted mean. Calculate the GPA for this transcript:

[tex]\[
\begin{tabular}{|c|c|}
\hline
Grades & \# of credit hours \\
\hline
B & 3 \\
B & 3 \\
B & 5 \\
C & 2 \\
\hline
\end{tabular}
\][/tex]

The grade point average is [tex]$\square$[/tex] (Round to the nearest hundredth as needed.)



Answer :

GinnyAnswer
Let's calculate the GPA step-by-step using the given data.

### Step 1: Assign grade points

We have the following grade points:
- [tex]\( A = 4 \)[/tex]
- [tex]\( B = 3 \)[/tex]
- [tex]\( C = 2 \)[/tex]
- [tex]\( D = 1 \)[/tex]
- [tex]\( F = 0 \)[/tex]

### Step 2: List the grades and their corresponding credit hours

Here are the grades received and their respective credit hours:
- [tex]\( B \)[/tex] with 3 credit hours
- [tex]\( B \)[/tex] with 3 credit hours
- [tex]\( B \)[/tex] with 5 credit hours
- [tex]\( C \)[/tex] with 2 credit hours

### Step 3: Calculate the products of grade points and credit hours

We multiply the grade points by the corresponding credit hours:
- For [tex]\( B \)[/tex] (3 points) with 3 credit hours: [tex]\( 3 \times 3 = 9 \)[/tex]
- For [tex]\( B \)[/tex] (3 points) with 3 credit hours: [tex]\( 3 \times 3 = 9 \)[/tex]
- For [tex]\( B \)[/tex] (3 points) with 5 credit hours: [tex]\( 3 \times 5 = 15 \)[/tex]
- For [tex]\( C \)[/tex] (2 points) with 2 credit hours: [tex]\( 2 \times 2 = 4 \)[/tex]

### Step 4: Calculate the total weighted sum of grade points

Add up all the products calculated in Step 3:
[tex]\[ 9 + 9 + 15 + 4 = 37 \][/tex]

### Step 5: Calculate the total number of credit hours

Add up all the credit hours:
[tex]\[ 3 + 3 + 5 + 2 = 13 \][/tex]

### Step 6: Calculate the GPA

Divide the total weighted sum of grade points by the total number of credit hours:
[tex]\[ \text{GPA} = \frac{37}{13} \approx 2.846 \][/tex]

### Step 7: Round the GPA to the nearest hundredth

[tex]\[ 2.846 \text{ rounds to } 2.85 \][/tex]

### Final Answer

The grade point average (GPA) is [tex]\( 2.85 \)[/tex].

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