Answer :
Sure, let's address each part of the question with a detailed, step-by-step solution.
### 1.1 Define the term profit according to the given context
In the context of Lucia's business, profit is the financial gain she obtains from selling her atchar. It is the difference between the total revenue she earns from sales and the total expenses she incurs (including the cost of the bucket of atchar, spices, and additional buckets). Essentially, if Lucia's revenue from selling the 2-litre buckets exceeds her total expenses, the surplus amount is her profit.
### 1.2 Calculate the VAT exclusive amount on Lucia's total expenses
Lucia's total expenses are made up of:
- A bucket of 20-litre atchar for R200
- Spices for R100
- 10 x 2-litre empty buckets for R40
All these prices include a 15% VAT. To find the VAT-exclusive amount, we need to remove the VAT from these amounts. The VAT-exclusive price can be calculated by dividing the VAT-inclusive price by 1.15 (since 15% VAT means the total amount is 115% of the base price).
- The VAT-inclusive total for all items is [tex]\( R200 + R100 + R40 = R340 \)[/tex].
- The VAT rate is 15%, so we divide by [tex]\( 1 + 0.15 = 1.15 \)[/tex].
The total VAT-exclusive amount is:
[tex]\[ \text{VAT-exclusive amount} = \frac{R340}{1.15} = R295.65 \][/tex]
Breaking it down into individual items:
- The VAT-exclusive amount for the bucket of 20-litre atchar is:
[tex]\[ \frac{R200}{1.15} = R173.91 \][/tex]
- The VAT-exclusive amount for the spices is:
[tex]\[ \frac{R100}{1.15} = R86.96 \][/tex]
- The VAT-exclusive amount for the 10 x 2-litre buckets is:
[tex]\[ \frac{R40}{1.15} = R34.78 \][/tex]
### 1.3 Verify if Lucia’s claim of making a profit of R300 from a 20-litre bucket is valid
1. Revenue Calculation:
- Lucia sells each 2-litre bucket for R60.
- She has a total of 20 litres of atchar.
- The number of 2-litre buckets she can fill is:
[tex]\[ \frac{20 \text{ litres}}{2 \text{ litres/bucket}} = 10 \text{ buckets} \][/tex]
- Her total revenue from selling these 10 buckets is:
[tex]\[ 10 \text{ buckets} \times R60 \text{ per bucket} = R600 \][/tex]
2. Expense Calculation:
- The VAT-exclusive total for a 20-litre bucket of atchar, spices, and 10 x 2-litre buckets is:
[tex]\[ R295.65 \][/tex]
3. Profit Calculation:
- Profit is determined by subtracting the total expenses from the total revenue:
[tex]\[ \text{Profit} = \text{Total Revenue} - \text{Total Expenses} \][/tex]
[tex]\[ \text{Profit} = R600 - R295.65 = R304.35 \][/tex]
### Conclusion
Lucia claimed that she would make a profit of R300. Upon verifying, her actual profit is R304.35. Therefore, Lucia's claim is valid, as her profit is slightly greater than R300.
### 1.1 Define the term profit according to the given context
In the context of Lucia's business, profit is the financial gain she obtains from selling her atchar. It is the difference between the total revenue she earns from sales and the total expenses she incurs (including the cost of the bucket of atchar, spices, and additional buckets). Essentially, if Lucia's revenue from selling the 2-litre buckets exceeds her total expenses, the surplus amount is her profit.
### 1.2 Calculate the VAT exclusive amount on Lucia's total expenses
Lucia's total expenses are made up of:
- A bucket of 20-litre atchar for R200
- Spices for R100
- 10 x 2-litre empty buckets for R40
All these prices include a 15% VAT. To find the VAT-exclusive amount, we need to remove the VAT from these amounts. The VAT-exclusive price can be calculated by dividing the VAT-inclusive price by 1.15 (since 15% VAT means the total amount is 115% of the base price).
- The VAT-inclusive total for all items is [tex]\( R200 + R100 + R40 = R340 \)[/tex].
- The VAT rate is 15%, so we divide by [tex]\( 1 + 0.15 = 1.15 \)[/tex].
The total VAT-exclusive amount is:
[tex]\[ \text{VAT-exclusive amount} = \frac{R340}{1.15} = R295.65 \][/tex]
Breaking it down into individual items:
- The VAT-exclusive amount for the bucket of 20-litre atchar is:
[tex]\[ \frac{R200}{1.15} = R173.91 \][/tex]
- The VAT-exclusive amount for the spices is:
[tex]\[ \frac{R100}{1.15} = R86.96 \][/tex]
- The VAT-exclusive amount for the 10 x 2-litre buckets is:
[tex]\[ \frac{R40}{1.15} = R34.78 \][/tex]
### 1.3 Verify if Lucia’s claim of making a profit of R300 from a 20-litre bucket is valid
1. Revenue Calculation:
- Lucia sells each 2-litre bucket for R60.
- She has a total of 20 litres of atchar.
- The number of 2-litre buckets she can fill is:
[tex]\[ \frac{20 \text{ litres}}{2 \text{ litres/bucket}} = 10 \text{ buckets} \][/tex]
- Her total revenue from selling these 10 buckets is:
[tex]\[ 10 \text{ buckets} \times R60 \text{ per bucket} = R600 \][/tex]
2. Expense Calculation:
- The VAT-exclusive total for a 20-litre bucket of atchar, spices, and 10 x 2-litre buckets is:
[tex]\[ R295.65 \][/tex]
3. Profit Calculation:
- Profit is determined by subtracting the total expenses from the total revenue:
[tex]\[ \text{Profit} = \text{Total Revenue} - \text{Total Expenses} \][/tex]
[tex]\[ \text{Profit} = R600 - R295.65 = R304.35 \][/tex]
### Conclusion
Lucia claimed that she would make a profit of R300. Upon verifying, her actual profit is R304.35. Therefore, Lucia's claim is valid, as her profit is slightly greater than R300.
