a student must have an average of at least 80 points on five tests to receive a b in a course the students grades on the first four test were 73,82,85,76 what scores on the last test will enable this students to receive a b or better in the course

To determine the minimum score the student needs on the fifth test to receive a B (with an average of at least 80), we can set up the problem as follows:

1. Let the score on the fifth test be \( x \).
2. The average of the five tests should be at least 80.

The formula for the average of the five tests is:

\[
\text{Average} = \frac{73 + 82 + 85 + 76 + x}{5} \geq 80
\]

First, calculate the sum of the first four test scores:

\[
73 + 82 + 85 + 76 = 316
\]

Now, substitute this sum into the formula:

\[
\frac{316 + x}{5} \geq 80
\]

To eliminate the fraction, multiply both sides by 5:

\[
316 + x \geq 400
\]

Next, solve for \( x \):

\[
x \geq 400 - 316
\]
\[
x \geq 84
\]

Thus, the student needs to score **at least 84** on the fifth test to achieve an average of 80 or higher.

Would you like more details, or do you have any questions?

Here are 5 related questions to further explore the concept:

1. What would the average be if the student scored exactly 84 on the fifth test?
2. If the student scored 90 on the fifth test, what would the final average be?
3. How would the required fifth test score change if the student's goal was an average of 85?
4. If the first four test scores were lower, how would that affect the required fifth test score?
5. What strategies can a student use to ensure they meet or exceed a target average across multiple tests?

**Tip:** When working with averages, it's often easier to calculate the required sum for all tests first, and then determine what remains to be achieved.

Learn how to calculate the minimum score required on the fifth test to achieve an average of at least 80 and receive a B grade. This problem involves calculating averages and solving inequalities based on test scores. Suitable for high school students.

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