A store mixes Brazilian coffee worth $11 per Kilogram, Turkish coffee worth $13 per kilogram. The mixture is to sell for $12 per kilogram. Can you help me find how much of each should be used to make a 564- Kilogram of both mixtures please and thank you.

Let the amounts be B and T kilograms.

B + T = 564

11 B + 13 T = 12(B + T) = 6768
11 B + 11 T = 6204
2 T = 564
T = 282
B = 282
(equal amounts of each)

To solve this problem, we can use a system of equations. Let's assume x kilograms of Brazilian coffee are used and y kilograms of Turkish coffee are used to make a final mixture of 564 kilograms.

Since the total weight of the mixture is 564 kilograms, we have the equation:

x + y = 564 -- (Equation 1)

The cost per kilogram of the Brazilian coffee is $11, and the cost per kilogram of the Turkish coffee is $13. The final mixture must have a cost per kilogram of $12.

To calculate the cost of the mixture, we can multiply the amount of Brazilian coffee by its cost and the amount of Turkish coffee by its cost, and then sum the two costs:

11x + 13y = 12 * 564 -- (Equation 2)

Now we have a system of equations and we can solve it using various methods, such as substitution or elimination. I will use the substitution method to solve it.

Let's solve Equation 1 for x:
x = 564 - y

Now substitute this value of x in Equation 2:

11(564 - y) + 13y = 12 * 564

Expand the equation:

6204 - 11y + 13y = 6768

Combine like terms:

2y = 564

Divide both sides by 2:

y = 282

Now, substitute the value of y back into Equation 1 to find x:

x + 282 = 564

x = 282

Therefore, to make a 564-kilogram mixture, you would need 282 kilograms of Brazilian coffee and 282 kilograms of Turkish coffee.

(Source: Own calculations)