Q1. Shureka Washburn has scores of 88, 74, 83, and 61 on her algebra tests. a. Use an inequality to find the scores she must make on the final exam to pass the course with an average of 77 or higher, given that the final exam counts as two tests. b. Explain the meaning of the answer to part (a).

Background

Topic: Solving Linear Inequalities and Averages

This question tests your ability to set up and solve an inequality involving averages, where one test (the final exam) counts as multiple tests. You will use algebraic reasoning to determine the minimum score needed on the final exam to achieve a target average.

Key Terms and Formulas

• Average: The sum of all scores divided by the number of tests.

• Inequality: A mathematical statement that shows the relationship between expressions that are not necessarily equal.

• Let be the score on the final exam.

Formula for average:

Step-by-Step Guidance

1. Assign a variable for the unknown: Let represent the score on the final exam.

2. Write an expression for the total score: Add the scores from the four tests and add for the final exam (since it counts as two tests). So, total score is .

3. Write the inequality for the average: The average must be at least 77, and there are 6 tests in total (4 regular + 2 for the final). So, set up the inequality:

4. Simplify the numerator by adding the known scores:

   , so the inequality becomes:

5. Multiply both sides of the inequality by 6 to eliminate the denominator:

Try solving on your own before revealing the answer!