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Sagot :
Sure, let's tackle each part of the question step-by-step:
### Part (a) - Completing the Table
We need to calculate the missing quantities and costs:
1. Glue Gun:
- Price per item (including 25% VAT): R 22.5
- Number required: 5
- Cost: R 22.5 5 = R 112.5
2. Glue sticks 1 kg:
- Price per item (including 25% VAT): R 160
- Total cost: R 2320
- Number required: [tex]\( \frac{R 2320}{R 160} = 14.5 \)[/tex]
- Thus, 14.5 glue sticks are needed.
3. Battery pack of 60:
- Price per item (including 25% VAT): R 199
- Number required: 2
- Given total cost: R 1398 (This seems like an error in the cost column, listed properly it should be R 398)
- Correct total cost should be: R 199 2 = R 398
4. Battery holder:
- Price per item (including 25% VAT): R 12.88
- Number required: 20
- Cost: R 12.88 20 = R 257.6
5. LED (pack of 300):
- Price per item (including 25% VAT): R 199
- Number required: 1
- Cost: R 199 1 = R 199
6. Buzzes:
- Price per item (including 25% VAT): R 13.23
- Number required: 20
- Cost: R 13.23 20 = R 264.6
7. Connecting wire per meter:
- Price per item (including 25% VAT): R 2
- Number required: 20
- Cost: R 2 20 = R 40
8. Resistor (pack of 10):
- Price per item (including 25% VAT): R 7.62
- Number required: 10
- Cost: R 7.62 10 = R 76.2
9. Paint per litre:
- Price per item (including 25% VAT): R 159
- Number required: 3
- Cost: R 159 3 = R 477
Now, the completed table should look like this:
[tex]\[ \begin{tabular}{|c|c|c|c|c|} \hline \text{Item No.} & \text{Tool / Equipment} & \text{\begin{tabular}{l} Price per Item \\ (including 25% VAT) \end{tabular}} & \text{\begin{tabular}{l} Number \\ required \end{tabular}} & \text{Cost} \\ \hline 1 & \text{Glue Gun} & R 22.5 & 5 & R 112.5 \\ \hline 2 & \text{Glue sticks 1 kg} & R 160 & 14.5 & R 2320 \\ \hline 3 & \text{\begin{tabular}{l} Battery pack of 60 \\ (Penonsing batteries) \end{tabular}} & R 199 & 2 & R 398 \\ \hline 4 & \text{Battery holder} & R 12.88 & 20 & R 257.6 \\ \hline 5 & \text{LED (pack of 300)} & R 199 & 1 & R 199 \\ \hline 6 & \text{Buzzes} & R 13.23 & 20 & R 264.6 \\ \hline 7 & \text{Connecting wire per meter} & R 2 & 20 & R 40 \\ \hline 8 & \text{Resistor (pack of 10)} & R 7.62 & 10 & R 76.2 \\ \hline 9 & \text{Paint per litre} & R 159 & 3 & R 477 \\ \hline \textbf{Total} & & & & \textbf{R 4144.9} \\ \hline \end{tabular} \][/tex]
### Part (b) - Total Cost of All Items
The total cost of all items is found by summing up all the individual costs:
[tex]\[ \text{Total cost} = R 112.5 + R 2320 + R 398 + R 257.6 + R 199 + R 264.6 + R 40 + R 76.2 + R 477 = R 4144.9 \][/tex]
### Part (c) - Total VAT Paid at 15%
To calculate the total VAT paid at 15%, we need to first remove the included 25% VAT to get the base cost and then apply 15% VAT to the base cost.
1. Remove the included 25% VAT:
[tex]\[ \text{Base cost} = \frac{\text{Total cost}}{1.25} = \frac{R 4144.9}{1.25} = R 3315.92 \][/tex]
2. Calculate the 15% VAT:
[tex]\[ \text{Total VAT paid} = \text{Base cost} \times 0.15 = R 3315.92 \times 0.15 = R 497.39 \][/tex]
So, the total VAT paid at 15% is R 497.39.
This completes the detailed, step-by-step solution to the problem.
### Part (a) - Completing the Table
We need to calculate the missing quantities and costs:
1. Glue Gun:
- Price per item (including 25% VAT): R 22.5
- Number required: 5
- Cost: R 22.5 5 = R 112.5
2. Glue sticks 1 kg:
- Price per item (including 25% VAT): R 160
- Total cost: R 2320
- Number required: [tex]\( \frac{R 2320}{R 160} = 14.5 \)[/tex]
- Thus, 14.5 glue sticks are needed.
3. Battery pack of 60:
- Price per item (including 25% VAT): R 199
- Number required: 2
- Given total cost: R 1398 (This seems like an error in the cost column, listed properly it should be R 398)
- Correct total cost should be: R 199 2 = R 398
4. Battery holder:
- Price per item (including 25% VAT): R 12.88
- Number required: 20
- Cost: R 12.88 20 = R 257.6
5. LED (pack of 300):
- Price per item (including 25% VAT): R 199
- Number required: 1
- Cost: R 199 1 = R 199
6. Buzzes:
- Price per item (including 25% VAT): R 13.23
- Number required: 20
- Cost: R 13.23 20 = R 264.6
7. Connecting wire per meter:
- Price per item (including 25% VAT): R 2
- Number required: 20
- Cost: R 2 20 = R 40
8. Resistor (pack of 10):
- Price per item (including 25% VAT): R 7.62
- Number required: 10
- Cost: R 7.62 10 = R 76.2
9. Paint per litre:
- Price per item (including 25% VAT): R 159
- Number required: 3
- Cost: R 159 3 = R 477
Now, the completed table should look like this:
[tex]\[ \begin{tabular}{|c|c|c|c|c|} \hline \text{Item No.} & \text{Tool / Equipment} & \text{\begin{tabular}{l} Price per Item \\ (including 25% VAT) \end{tabular}} & \text{\begin{tabular}{l} Number \\ required \end{tabular}} & \text{Cost} \\ \hline 1 & \text{Glue Gun} & R 22.5 & 5 & R 112.5 \\ \hline 2 & \text{Glue sticks 1 kg} & R 160 & 14.5 & R 2320 \\ \hline 3 & \text{\begin{tabular}{l} Battery pack of 60 \\ (Penonsing batteries) \end{tabular}} & R 199 & 2 & R 398 \\ \hline 4 & \text{Battery holder} & R 12.88 & 20 & R 257.6 \\ \hline 5 & \text{LED (pack of 300)} & R 199 & 1 & R 199 \\ \hline 6 & \text{Buzzes} & R 13.23 & 20 & R 264.6 \\ \hline 7 & \text{Connecting wire per meter} & R 2 & 20 & R 40 \\ \hline 8 & \text{Resistor (pack of 10)} & R 7.62 & 10 & R 76.2 \\ \hline 9 & \text{Paint per litre} & R 159 & 3 & R 477 \\ \hline \textbf{Total} & & & & \textbf{R 4144.9} \\ \hline \end{tabular} \][/tex]
### Part (b) - Total Cost of All Items
The total cost of all items is found by summing up all the individual costs:
[tex]\[ \text{Total cost} = R 112.5 + R 2320 + R 398 + R 257.6 + R 199 + R 264.6 + R 40 + R 76.2 + R 477 = R 4144.9 \][/tex]
### Part (c) - Total VAT Paid at 15%
To calculate the total VAT paid at 15%, we need to first remove the included 25% VAT to get the base cost and then apply 15% VAT to the base cost.
1. Remove the included 25% VAT:
[tex]\[ \text{Base cost} = \frac{\text{Total cost}}{1.25} = \frac{R 4144.9}{1.25} = R 3315.92 \][/tex]
2. Calculate the 15% VAT:
[tex]\[ \text{Total VAT paid} = \text{Base cost} \times 0.15 = R 3315.92 \times 0.15 = R 497.39 \][/tex]
So, the total VAT paid at 15% is R 497.39.
This completes the detailed, step-by-step solution to the problem.
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