Answer :
Final Answer:
You need to mix approximately 69.44 kg of brand A coffee with 126 kg of brand B coffee to create a mixture costing 24 rupees per kg.
Explanation:
To find out how many kilograms of brand A coffee (let's call it 'x' kg) must be mixed with 126 kg of brand B coffee to achieve a mixture costing 24 rupees per kg, we can set up the following equation:
(Price of A × x kg + Price of B × 126 kg) / (x kg + 126 kg) = 24 rupees/kg
Now, plug in the prices:
(36.60x + 17.10 × 126) / (x + 126) = 24
Multiply both sides by (x + 126) to get rid of the denominator:
36.60x + 17.10 × 126 = 24 × (x + 126)
Now, solve for 'x':
36.60x + 2148.60 = 24x + 3024
Rearrange and simplify:
36.60x - 24x = 3024 - 2148.60
12.60x = 875.40
Now, divide by 12.60 to find 'x':
x = 875.40 / 12.60
x ≈ 69.44 kg
So, you need to mix approximately 69.44 kg of brand A coffee with 126 kg of brand B coffee to get a mixture that costs 24 rupees per kg.
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Final answer:
In order to find out how many kilograms of Brand A coffee must be mixed with Brand B coffee to get a mixture costing 24 Rs per kg, create an equation representing a weighted average. The answer will be obtained by solving this equation.
Explanation:
We're looking to find out how much of Brand A coffee must be mixed with Brand B coffee. To find this, we'll look at a weighted average. This is a common problem in algebra.
Let's denote x as the amount (in kg) of Brand A coffee. The total cost of the mixture will be (x kg * 36.6 Rs/kg) + (126 kg * 17.1 Rs/kg). The average cost of the mixture will be this total cost divided by the total weight, which is (x + 126) kg.
The equation will then become: (x*36.6 + 126*17.1) / (x + 126) = 24.
Multiply both sides by (x+126) to get rid of the denominator, which results in: x*36.6 + 126*17.1 = 24*(x+126).
Solve this equation to find out the amount in kg of Brand A coffee.
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