A store mixes Kenyan coffee worth $11 per kilogram and Turkish coffee worth $13 per kilogram. The mixture is to sell for $12 per kilogram. Find how much of each should be used to make a 348-kilogram mixture. How many kilograms of the Kenyan coffee should be in the mixture?
11K + 13T = 12*348
but K+T=348, so
11K + 13(348-K) = 12*348
K = 174
as expected, since the final price is the average of the two kinds, there is an equal amount of each.
To find out how much of each type of coffee should be used to make a 348-kilogram mixture, we can set up a system of equations based on the given information.
Let's assume x kilograms of Kenyan coffee is used and y kilograms of Turkish coffee is used.
From the problem, we know that the mixture is to sell for $12 per kilogram. This means that the total cost of the mixture should be equal to the cost per kilogram multiplied by the total weight of the mixture. We can write this equation as:
11x + 13y = 12 * 348
Additionally, we know that the total weight of the mixture should be 348 kilograms. This gives us another equation:
x + y = 348
Now, we can solve this system of equations to find the values of x and y.
We can start by multiplying the second equation by 11 to eliminate the x variable:
11x + 11y = 11 * 348
Next, subtract this new equation from the first equation:
(11x + 13y) - (11x + 11y) = 12 * 348 - 11 * 348
This simplifies to:
2y = 12 * 348 - 11 * 348
2y = 348
Divide both sides of the equation by 2:
y = 348 / 2
y = 174
Now, substitute the value of y back into the second equation to find x:
x + 174 = 348
x = 348 - 174
x = 174
So, 174 kilograms of Kenyan coffee should be used in the mixture.
Therefore, the mixture should contain 174 kilograms of Kenyan coffee and 174 kilograms of Turkish coffee.