Z scored 8 out of 40 in Term I and scored 12 out of 40 in Term 2. If the average Pass percentage is 35% of the average of all Terms, how much should Z score in Term 3 out of 100?  

To determine how much Z should score in Term 3 out of 100 to pass, we follow these steps:

### Step 1: Calculate the average score for Terms 1 and 2
- Z's scores:
  - Term 1: 8 out of 40
  - Term 2: 12 out of 40

Convert these scores to percentages:
\[
\text{Term 1 percentage} = \frac{8}{40} \times 100 = 20\%
\]
\[
\text{Term 2 percentage} = \frac{12}{40} \times 100 = 30\%
\]

### Step 2: Calculate the average of the first two terms
\[
\text{Average percentage for Terms 1 and 2} = \frac{20\% + 30\%}{2} = 25\%
\]

### Step 3: Determine the pass percentage based on the average of all terms
The pass percentage is 35% of the average of all three terms. Let \( x \) be the score out of 100 in Term 3.

Convert the score in Term 3 to a percentage:
\[
\text{Term 3 percentage} = \frac{x}{100} \times 100 = x\%
\]

The average percentage for all three terms is:
\[
\text{Average percentage for all terms} = \frac{20\% + 30\% + x\%}{3} = \frac{50\% + x\%}{3}
\]

The pass percentage is 35% of this average:
\[
\text{Pass percentage} = 0.35 \times \frac{50\% + x\%}{3}
\]

For Z to pass, the score in Term 3 must satisfy:
\[
x\% \geq 0.35 \times \frac{50\% + x\%}{3} \times 100 
\]

### Step 4: Solve for \( x \)

For Z to achieve a pass mark, we rearrange and simplify to solve for \( x \):

To solve this equation:

\[
x \geq \frac{20\% + x\%}{3} \times 35
\]

This will give us the minimum score required by Z in Term 3 out of 100.

### Would you like further explanation or have any questions? 
Here are five related questions you might consider:

1. What is the minimum passing score in each term?
2. How do percentages relate to grades in multiple terms?
3. What if the pass percentage was higher than 35%?
4. How does Term 3’s weight affect the overall outcome?
5. Could the pass criteria change if the terms have different maximum scores?

**Tip:** Understanding how averages work across multiple scores helps in planning and improving overall performance!

Discover how to calculate the score needed in Term 3 for passing based on scores from Terms 1 and 2. Understand percentages and averages in academic assessments.

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