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The problem states that a teacher assigns 20% of the final score for the assignment and 80% for the test. A student scored 80 marks for the assignment, and his final score is 72. We are asked to find the marks he scored on the test.

Let’s break it down:

1. The final score \( F \) is composed of:
   - 20% from the assignment score \( A \),
   - 80% from the test score \( T \).

The formula for the final score is:
\[
F = 0.2A + 0.8T
\]
We are given:
- \( F = 72 \) (final score),
- \( A = 80 \) (assignment score).

Now, substitute the known values into the formula:
\[
72 = 0.2(80) + 0.8T
\]
First, calculate \( 0.2 \times 80 \):
\[
0.2 \times 80 = 16
\]
Now the equation becomes:
\[
72 = 16 + 0.8T
\]
Subtract 16 from both sides:
\[
72 - 16 = 0.8T
\]
\[
56 = 0.8T
\]
Finally, divide both sides by 0.8 to solve for \( T \):
\[
T = \frac{56}{0.8} = 70
\]

So, the marks he scored on the test are **70**.

Do you need any further details or explanations on this? 

Here are 5 related questions to extend this concept:
1. If another student scored 85 on the assignment and had a final score of 76, what did they score on the test?
2. How would the formula change if the assignment weighed 30% and the test weighed 70%?
3. If the student scored 65 on the test but had the same assignment score, what would their final score be?
4. How would the test score change if the student’s final score was 10 points higher with the same assignment score?
5. What would happen to the final score if the assignment weight increased to 50%?

**Tip**: Always verify if you need to manipulate percentages in exams and assignments by converting them into decimal form before solving equations.

A teacher assigns each student a final score of 20% for the assignment and 80% for the test. One student scored 80 marks for the assignment. His final score is 72. What are the marks he scored for the test?

Explore how to calculate test scores using weighted averages in educational grading, where the assignment contributes 20% and the test 80% to the final grade. This example uses algebraic techniques to solve for the unknown test score when the assignment score and final grade are known.

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