Westonci.ca connects you with experts who provide insightful answers to your questions. Join us today and start learning! Discover in-depth answers to your questions from a wide network of experts on our user-friendly Q&A platform. Explore comprehensive solutions to your questions from a wide range of professionals on our user-friendly platform.
Sagot :
Certainly! Let's solve this step-by-step:
### Step 1: Calculate the Cost Price per Kilogram
We know the trader sells the mixture for Ksh 48 per kilogram and makes a 60% profit. Let's determine the cost price per kilogram of the mixture.
Given:
- Selling price per kg = Ksh 48
- Profit percentage = 60%
We can calculate the cost price per kilogram using the formula:
[tex]\[ \text{Cost Price (CP) per kg} = \frac{\text{Selling Price}}{1 + \text{Profit Percentage}} \][/tex]
Substituting the values, we get:
[tex]\[ \text{CP per kg} = \frac{48}{1 + 0.60} = \frac{48}{1.6} = 30 \text{ Ksh} \][/tex]
### Step 2: Set up the Mixture Equation
Let [tex]\( x \)[/tex] be the proportion of maize in the mixture, and [tex]\( 1 - x \)[/tex] be the proportion of beans in the mixture. The cost price per kg of the mixture can be determined by the weighted average of the costs of maize and beans.
Given:
- Cost of maize per kg = Ksh 20
- Cost of beans per kg = Ksh 60
The equation for the cost price of the mixture is:
[tex]\[ \text{Cost Price per kg} = 20x + 60(1 - x) \][/tex]
Substituting the calculated cost price:
[tex]\[ 30 = 20x + 60(1 - x) \][/tex]
### Step 3: Solve for [tex]\( x \)[/tex]
Simplify the equation:
[tex]\[ 30 = 20x + 60 - 60x \][/tex]
[tex]\[ 30 = 60 - 40x \][/tex]
[tex]\[ 40x = 60 - 30 \][/tex]
[tex]\[ 40x = 30 \][/tex]
[tex]\[ x = \frac{30}{40} = \frac{3}{4} = 0.75 \][/tex]
So, the proportion of maize in the mixture is [tex]\( 0.75 \)[/tex] (or 75%).
### Step 4: Determine the Proportion of Beans
The proportion of beans is:
[tex]\[ 1 - x = 1 - 0.75 = 0.25 \][/tex]
So, the proportion of beans in the mixture is [tex]\( 0.25 \)[/tex] (or 25%).
### Step 5: Calculate the Ratio of Maize to Beans
The ratio of maize to beans per kilogram is:
[tex]\[ \text{Ratio (Maize:Beans)} = \frac{\text{Proportion of Maize}}{\text{Proportion of Beans}} = \frac{0.75}{0.25} = 3 \][/tex]
### Conclusion:
The ratio of maize to beans per kilogram in the mixture is [tex]\( 3:1 \)[/tex].
### Step 1: Calculate the Cost Price per Kilogram
We know the trader sells the mixture for Ksh 48 per kilogram and makes a 60% profit. Let's determine the cost price per kilogram of the mixture.
Given:
- Selling price per kg = Ksh 48
- Profit percentage = 60%
We can calculate the cost price per kilogram using the formula:
[tex]\[ \text{Cost Price (CP) per kg} = \frac{\text{Selling Price}}{1 + \text{Profit Percentage}} \][/tex]
Substituting the values, we get:
[tex]\[ \text{CP per kg} = \frac{48}{1 + 0.60} = \frac{48}{1.6} = 30 \text{ Ksh} \][/tex]
### Step 2: Set up the Mixture Equation
Let [tex]\( x \)[/tex] be the proportion of maize in the mixture, and [tex]\( 1 - x \)[/tex] be the proportion of beans in the mixture. The cost price per kg of the mixture can be determined by the weighted average of the costs of maize and beans.
Given:
- Cost of maize per kg = Ksh 20
- Cost of beans per kg = Ksh 60
The equation for the cost price of the mixture is:
[tex]\[ \text{Cost Price per kg} = 20x + 60(1 - x) \][/tex]
Substituting the calculated cost price:
[tex]\[ 30 = 20x + 60(1 - x) \][/tex]
### Step 3: Solve for [tex]\( x \)[/tex]
Simplify the equation:
[tex]\[ 30 = 20x + 60 - 60x \][/tex]
[tex]\[ 30 = 60 - 40x \][/tex]
[tex]\[ 40x = 60 - 30 \][/tex]
[tex]\[ 40x = 30 \][/tex]
[tex]\[ x = \frac{30}{40} = \frac{3}{4} = 0.75 \][/tex]
So, the proportion of maize in the mixture is [tex]\( 0.75 \)[/tex] (or 75%).
### Step 4: Determine the Proportion of Beans
The proportion of beans is:
[tex]\[ 1 - x = 1 - 0.75 = 0.25 \][/tex]
So, the proportion of beans in the mixture is [tex]\( 0.25 \)[/tex] (or 25%).
### Step 5: Calculate the Ratio of Maize to Beans
The ratio of maize to beans per kilogram is:
[tex]\[ \text{Ratio (Maize:Beans)} = \frac{\text{Proportion of Maize}}{\text{Proportion of Beans}} = \frac{0.75}{0.25} = 3 \][/tex]
### Conclusion:
The ratio of maize to beans per kilogram in the mixture is [tex]\( 3:1 \)[/tex].
We hope you found this helpful. Feel free to come back anytime for more accurate answers and updated information. Thank you for visiting. Our goal is to provide the most accurate answers for all your informational needs. Come back soon. Keep exploring Westonci.ca for more insightful answers to your questions. We're here to help.