Question

Use the following for questions 24-25. Sylvia has credit hours and grades as shown on the chart. Her school gives 4 points for an \(A, 3\) points for a \(B, 2\) points for a \(C, 1\) point for a \(D\), and nothing for an \(F\). $$ \begin{array}{|c|c|c|c|c|c|} \hline \text { Grades } & \text { A } & \text { B } & \text { C } & \text { D } & \text { F } \\ \hline \text { Credit hours } & 16 & 27 & 18 & 8 & 1 \\ \hline \begin{array}{c} \text { Grade points } \\ \text { per credit } \\ \text { hour } \end{array} & 4 & 3 & 2 & 1 & 0 \\ \hline \end{array} $$How many total grade points did Sylvia earn from As and Bs combined? A. 27 B. 64 C. 81 D. 145

Short answer

145

Step-by-step solution

- Identify Credit Hours and Grade Points for As

Sylvia has 16 credit hours for As. Each A earns 4 grade points per credit hour.

- Calculate Grade Points for As

Multiply the number of credit hours for As by the grade points per credit hour: \[ 16 \text{ credit hours} \times 4 \text{ points per credit hour} = 64 \text{ grade points} \]

- Identify Credit Hours and Grade Points for Bs

Sylvia has 27 credit hours for Bs. Each B earns 3 grade points per credit hour.

- Calculate Grade Points for Bs

Multiply the number of credit hours for Bs by the grade points per credit hour: \[ 27 \text{ credit hours} \times 3 \text{ points per credit hour} = 81 \text{ grade points} \]

- Add Grade Points for As and Bs

Add the grade points earned from As and Bs: \[ 64 \text{ grade points (from As) } + 81 \text{ grade points (from Bs) } = 145 \text{ total grade points} \]

Key concepts

grade points calculation

Grade points calculation is a critical component of understanding academic performance. To find out how many grade points a student earns, you need to consider both the credits for each grade and the grade points per credit. In Sylvia's case, she has various grades each associated with different points per credit.
To calculate the grade points for each letter grade:

• Multiply the number of credit hours by the grade points per credit.

If a student has several grades, you need to calculate the grade points for each and then sum the totals. This method helps you determine how well a student is performing overall.

credit hours

Credit hours are essential in calculating GPA and understanding a student's workload. A credit hour typically signifies one hour of classroom instruction plus two hours of out-of-class work each week for one term.
Understanding Sylvia's situation:

• She has a specific number of credit hours for each grade.
• For example, she has 16 credit hours for As and 27 credit hours for Bs.
• These numbers represent the weight of each grade in her overall academic performance.

Knowing the credit hours for each grade category allows better calculation of the total grade points.

multiplication and addition

Multiplication and addition are fundamental arithmetic operations used throughout the grade points calculation process. Here is how you apply them in this context:
First, use multiplication to calculate the grade points for each grade:

• For As: Multiply the credit hours (16) by the points per credit hour (4). \( 16 \times 4 = 64 \).
• For Bs: Multiply the credit hours (27) by the points per credit hour (3). \( 27 \times 3 = 81 \).

Next, use addition to find the combined total of these grade points:

• Add the grade points for As and Bs: \( 64 + 81 = 145 \).

By mastering these operations, you'll efficiently calculate total grade points and other academic measures.