Question

Terri has grades of 75, 87, 96, 75, and 88 prior to the final exam in her math class. If all the grades are weighted equally, what would Terri need to make on the final exam to average an $A$ in the class ( $A$ ranges between 90 and 100 points)? A. 90 B. 95 C. 100 D. It is impossible for her to get an A with those grades.

Short answer

It is impossible for Terri to get an A with those grades.

Step-by-step solution

- Understand the Problem

To determine what grade Terri needs to score on her final exam to average an A (90-100 points) in the class, calculate the average of her current grades and see what score she needs to achieve the target average.

- Calculate the Current Average

Add up all the grades Terri currently has and then divide by the number of grades (i.e., 5). This will give the current average before the final exam. Current Grades: 75, 87, 96, 75, 88 Sum: 75 + 87 + 96 + 75 + 88 = 421 Current Average: \ $\frac{421}{5}=84.2$

- Use the Weighted Average Formula

The final exam grade will be added to the current total grades and divided by the number of grades including the final exam (6 grades). Set up the equation: Let x be the score Terri needs on the final exam. \ $\frac{421+x}{6}\ge 90$

- Solve the Equation

Solve for x to find the minimum grade needed on the final exam to achieve an average of 90: \ $\frac{421+x}{6}=90$ Multiply both sides by 6: \ 421 + x = 540 Subtract 421 from both sides: \ x = 540 - 421 = 119 \

- Interpret the Result

Since 119 is greater than 100, it is impossible for Terri to score this on the final exam. Thus, it is impossible for her to get an A with her current grades.

Key concepts

Weighted Average

A weighted average is a measure that takes into account the different weights or importance of various data points. It's particularly useful when dealing with grades or scores from different assignments with unequal importance.
To calculate a weighted average, you multiply each data point by its respective weight, add all these products together, and divide by the total sum of weights.
For instance, if different assignments in a course have different levels of importance, like quizzes, midterms, and finals, each of these categories will contribute differently to the final grade.
Understanding the concept of weighted average is crucial for precisely calculating overall scores in many scenarios.

Grade Calculation

Grade calculation often involves more than just averaging a set of scores. It may require understanding different grading weights and the impact of each score.
In Terri's case, we calculated the average of her current grades before considering the final exam.
Here's how you approach it step-by-step:

• List all current grades and sum them: 75 + 87 + 96 + 75 + 88.
• Divide the sum by the number of grades: $\frac{421}{5}=84.2$.

Terri's current average is 84.2, and we use this to calculate the required score on her final exam to achieve a higher target average.

Mathematical Reasoning

Mathematical reasoning involves logically thinking through a problem to arrive at a solution. It requires understanding the problem, selecting relevant mathematical tools, and applying these tools appropriately.
For Terri's grade calculation, we applied mathematical reasoning in these ways:

• Identifying the target average for an A, which is between 90 and 100.
• Setting up an equation that includes her current grades and the unknown final exam grade: $\frac{421+x}{6}$.
• Solving the equation step-by-step to find that x must be 119.

Using mathematical reasoning helps solve such problems systematically and accurately.

GED Math

GED math problems often cover topics like basic arithmetic, algebra, and data analysis.
Understanding concepts such as averages, weighted averages, and equations is essential for success.
Here's how Terri's problem aligns with GED Math topics:

• Basic Arithmetic: Adding and dividing numbers to find the average.
• Algebra: Setting up and solving an equation to find the required exam score.
• Data Analysis: Understanding grades as data points and calculating an overall average.

By mastering these fundamental concepts, students can handle a wide range of questions they might encounter on the GED test.