To find the selling price per kg of the mixture, let's first determine the cost price per kg of the mixture.
Step 1: Determine the total cost of each type of floor.
Let’s assume that the trader mixes \(1\) kg of the first type, \(2\) kg of the second type, and \(3\) kg of the third type.
Costs:
- First type (shs 12 per kg): \( 1, \text{kg} \times 12, \text{shs} = 12, \text{shs} \)
- Second type (shs 18 per kg): \( 2, \text{kg} \times 18, \text{shs} = 36, \text{shs} \)
- Third type (shs 15 per kg): \( 3, \text{kg} \times 15, \text{shs} = 45, \text{shs} \)
Step 2: Calculate total cost.
Now, we can find the total cost of the mixture: \[ \text{Total cost} = 12, \text{shs} + 36, \text{shs} + 45, \text{shs} = 93, \text{shs} \]
Step 3: Calculate total weight of the mixture.
The total weight of the mixture is: \[ \text{Total weight} = 1, \text{kg} + 2, \text{kg} + 3, \text{kg} = 6, \text{kg} \]
Step 4: Calculate cost price per kg.
Now, we can calculate the cost price per kg of the mixture: \[ \text{Cost price per kg} = \frac{\text{Total cost}}{\text{Total weight}} = \frac{93, \text{shs}}{6, \text{kg}} = 15.5, \text{shs per kg} \]
Step 5: Calculate selling price with profit.
Next, the trader wants to sell the mixture at a 20% profit: \[ \text{Profit} = 20% = 0.20 \] \[ \text{Selling price per kg} = \text{Cost price per kg} + \text{Profit on cost price per kg} \] \[ \text{Selling price per kg} = 15.5, \text{shs} + (0.20 \times 15.5, \text{shs}) \] Calculating the profit: \[ 0.20 \times 15.5 = 3.1, \text{shs} \] So, \[ \text{Selling price per kg} = 15.5, \text{shs} + 3.1, \text{shs} = 18.6, \text{shs} \]
Conclusion
The selling price per kg of the mixture is 18.6 shs.