Problem 130 - College Algebra Essentials

Question

Use the strategy for solving word problems, modeling the verbal conditions of the problem with a linear inequality. To earn an A in a course, you must have a final average of at least \(90 \% .\) On the first four examinations, you have grades of \(86 \%, 88 \%, 92 \%,\) and \(84 \% .\) If the final examination counts as two grades, what must you get on the final to earn an A in the course?

Step-by-Step Solution

Answer

The minimum grade on the final exam to earn an A in the course is 95%.

Step 1: Understand the problem

There are four known exam grades: 86%, 88%, 92% and 84%. The final exam counts as two grades. The goal is to find what grade on the final exam will yield an average of at least 90%.

Step 2: Set up the inequality

Over six exams, an average of at least 90% equates to a total of at least \(6 \times 90 = 540\% .\) Letting \(X\) represent the grade needed on the final exam, the inequality can be written as \(86 + 88 + 92 + 84 + X + X \geq 540\). Simplifying this gives \(2X + 350 \geq 540 .\)

Step 3: Solve the inequality

Subtracting 350 from both sides gives \(2X \geq 190\) and dividing both sides by 2 gives \(X \geq 95\%\).