A store mixes Kenyan Coffee worth $11 per Kilogram and venezuelan coffee worth $14 per Kilogram. The mixture is to sell for $12 per kilogram. Find out how much of each should be used to make a 396-Kilogram Mixture
Work with the total dollar value of the coffees.
Let K be the amount of Kenyan coffee
V is the Venezuelan coffee
K+V=396
11K + 14(396-K) = 12*396
11K + 14*396 - 14K = 12*396
3K = 2*396 = 792
K = 264
V = 132
To find out how much of each coffee should be used to make a 396-kilogram mixture, we can set up a system of equations based on the given information.
Let's assume x represents the amount of Kenyan coffee (in kilograms) and y represents the amount of Venezuelan coffee (in kilograms) in the mixture.
According to the given information, the store wants to sell a 396-kilogram mixture. So we have the equation:
x + y = 396 -- Equation 1
The cost per kilogram of the Kenyan coffee is $11, while the cost per kilogram of the Venezuelan coffee is $14. The mixture is supposed to sell at $12 per kilogram. Therefore, we can calculate the total value of the two coffees in the mixture using the equation:
11x + 14y = 12 * 396 -- Equation 2
Now we can solve this system of equations to find the values of x and y.
Using Equation 1, we can solve for x:
x = 396 - y
Substituting this value of x in Equation 2, we get:
11(396 - y) + 14y = 12 * 396
Expanding the equation:
4356 - 11y + 14y = 4752
Combining like terms:
3y = 396
Dividing both sides by 3:
y = 132
Substituting this value of y back into Equation 1, we get:
x + 132 = 396
x = 396 - 132
x = 264
Therefore, to make a 396-kilogram mixture, the store should use 264 kilograms of Kenyan coffee and 132 kilograms of Venezuelan coffee.