https://file.aiquickdraw.com/mathbot/file/17271703119276v10mqo4.jpg

Let's break down the problem.

### Given:
- Jethro has sat 5 tests.
- Each test is marked out of 100.
- The mean (average) mark for the 5 tests is 74.

Thus, the total marks Jethro has scored in the 5 tests is:
\[
\text{Total marks for 5 tests} = 5 \times 74 = 370.
\]

Jethro is sitting one more test, and he wants the mean mark for all 6 tests to be at least 77.

### To find:
The minimum mark Jethro needs to get in the last test.

Let the mark Jethro needs in the last test be \( x \). For the mean of all 6 tests to be 77, the total marks for all 6 tests should be:
\[
\text{Total marks for 6 tests} = 6 \times 77 = 462.
\]

Therefore, the equation becomes:
\[
370 + x = 462.
\]

Solving for \( x \):
\[
x = 462 - 370 = 92.
\]

### Conclusion:
Jethro needs to score at least **92** in the last test to achieve a mean mark of 77 across all 6 tests.

Would you like a more detailed explanation or have any further questions?

---

Here are 5 related questions you could explore:
1. What would happen if Jethro wanted an average of 80 across all 6 tests?
2. How would the result change if the mean for the 5 tests was higher, say 78?
3. What if the last test was marked out of 150 instead of 100?
4. How can you calculate the mean if you have the individual scores for each test?
5. How would the scenario change if Jethro needed to maintain a certain grade in all subjects?

**Tip:** When calculating averages, always remember that the sum of all individual scores divided by the number of scores gives you the mean.

Jethro has sat 5 tests. Each test was marked out of 100, and Jethro's mean mark for the 5 tests is 74. Jethro has to sit one more test that is also to be marked out of 100. Jethro wants his mean mark for all 6 tests to be at least 77. Work out the least mark that Jethro needs to get for the last test.

Solve a problem where Jethro needs a minimum score on his final test to achieve an average of 77 across 6 tests. This problem covers concepts such as averages and basic algebra, suitable for students in Grades 6-8.

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