Eric has scores of 71, 83, and 84 on his history tests. Use an inequality to find the scores he can make on his final exam to receive a B in the class. The final exam counts as three ​tests, and a B is received if the final course average is greater than or equal to 80.

To solve this, let's denote Eric's final exam score as \( x \).

Since the final exam counts as three tests, we treat Eric's current test scores (71, 83, and 84) as if he has taken 6 tests in total, where the final exam score \( x \) is repeated three times in the calculation.

The condition for receiving a B is that the average score must be greater than or equal to 80. This leads us to the following inequality for the average score:

\[
\frac{71 + 83 + 84 + 3x}{6} \geq 80
\]

### Step-by-step Solution:
1. Sum the current test scores:
   \[
   71 + 83 + 84 = 238
   \]

2. Set up the inequality:
   \[
   \frac{238 + 3x}{6} \geq 80
   \]

3. Multiply both sides of the inequality by 6 to eliminate the denominator:
   \[
   238 + 3x \geq 480
   \]

4. Subtract 238 from both sides:
   \[
   3x \geq 242
   \]

5. Divide both sides by 3 to solve for \( x \):
   \[
   x \geq \frac{242}{3} \implies x \geq 80.67
   \]

### Conclusion:
Eric needs to score at least **80.67** on his final exam to receive a B in the class. Since exam scores are typically whole numbers, he would need to score at least **81** on his final exam to achieve a B.

---

Do you want any additional details or clarifications?

Here are some related questions:
1. What happens if Eric scores lower than 81 on the final exam?
2. How would the required score change if Eric had an extra test with a score of 75?
3. What if the final exam counts as two tests instead of three?
4. What score would Eric need if the requirement for a B was an average of 85 instead of 80?
5. How much would each test count if the final exam were only worth as much as one test?

**Tip:** Always double-check whether the final exam counts as one test or multiple tests, as this can significantly change the calculation.

Eric has scores of 71, 83, and 84 on his history tests. Use an inequality to find the scores he can make on his final exam to receive a B in the class. The final exam counts as three tests, and a B is received if the final course average is greater than or equal to 80.

Discover how to solve an inequality to find the minimum score Eric needs on his final exam to achieve a B in his history class. This problem involves using algebraic techniques and calculating averages with weighted exams, suitable for Grades 8-10.

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