Convert 6.5% to a common fraction and calculate the number of students who went on a tour if 200 students planned to go.

$$\frac{65 \div 5}{1000 \div 5} = \frac{13}{200}$$

The simplified common fraction is $\boxed{\frac{13}{200}}$.

1.1.2

$$\text{Number of learners who went} = \text{Total learners planned} - \text{Number of learners who did not go}$$ $$\text{Number of learners who went} = 200 - 13 = 187$$

The number of learners who went on a tour is $\boxed{187}$.

1.1.3

$$\text{Learners who went} = 187$$ $$\text{Learners who planned} = 200$$

$$\text{Ratio} = \text{Learners who went} : \text{Learners who planned} = 187 : 200$$

This ratio cannot be simplified further as 187 is a prime number and 200 is not a multiple of 187.
The simplified ratio is $\boxed{187 : 200}$.

1.1.4

$$\text{Number of learners who did not go} = 13$$ $$\text{Total learners planned} = 200$$

$$\text{Probability (percentage)} = \frac{13}{200} \times 100\% = 0,065 \times 100\% = 6,5\%$$

The probability is $\boxed{6,5\%}$.

Question 1.2

1.2.1

David was born in February 1998. In April 2023, he has already had his birthday.

$$\text{David's age} = 2023 - 1998 = 25 \text{ years old}$$

Sam was born in March 1993. In April 2023, he has already had his birthday.

$$\text{Sam's age} = 2023 - 1993 = 30 \text{ years old}$$

David's age is $\boxed{25 \text{ years}}$ and Sam's age is $\boxed{30 \text{ years}}$.

1.2.2

$$\text{Sam's share} = \frac{6}{11} \times R409\,750 = R223\,500$$

David will receive $\boxed{R186\,250}$ and Sam will receive $\boxed{R223\,500}$.

Question 1.3

1.3.1

The 'VAT' acronym in full is $\boxed{\text{Value Added Tax}}$.

1.3.2

$$\text{Cost per packet} = R38,99$$ $$\text{Total cost before VAT} = 15 \times R38,99 = R584,85$$

$$\text{VAT amount} = \text{Total cost before VAT} \times \text{VAT rate}$$ $$\text{VAT amount} = R584,85 \times 15\% = R584,85 \times 0,15 = R87,7275$$

$$\text{VAT amount} \approx R87,73$$

The amount of VAT she paid is $\boxed{R87,73}$.

1.3.3

$$\text{Total amount paid} = \text{Total cost before VAT} + \text{VAT amount}$$ $$\text{Total amount paid} = R584,85 + R87,73 = R672,58$$

The total amount she paid for the above items is $\boxed{R672,58}$.