To solve the problem, we need to find the score that Bob must earn on his sixth test so that his average score for all six tests is 80.

Step-by-Step Solution:

1. Sum of the First 5 Scores: Bob’s first five test scores are:

   • 72, 86, 92, 63, 77.

   The sum of these five scores is: $72 + 86 + 92 + 63 + 77 = 390.$

2. Total Sum for an Average of 80: The formula for the average score is: $\text{Average} = \frac{\text{Total Sum of Scores}}{\text{Number of Tests}}.$ Since Bob wants his average to be 80 for 6 tests, the total sum for all six tests must be: $80 \times 6 = 480.$

3. Score Needed on the Sixth Test: Let $x$ represent the score Bob needs on his sixth test. We can write the equation: $390 + x = 480.$ Solving for $x$: $x = 480 - 390 = 90.$

Conclusion:

Bob needs to score 90 on his sixth test in order to have an average of 80.

Would you like any further details or clarifications?

Here are some related questions:

1. How would Bob's average change if his sixth score was higher than 90?
2. What would the new average be if Bob scored only 70 on his sixth test?
3. What is the formula to calculate the average if the number of tests is different?
4. How does changing one score affect the overall average?
5. What is the minimum score Bob can get on his sixth test to pass with an average of at least 75?

Tip: Always check your work by recalculating the sum and ensuring that it matches the desired outcome when calculating averages.