a store mixes kenyan coffee worth $11 per kilogram and turkish coffee worth $13 per kilo gram. The mixture is to sell for $12 per kilogram. Find how much of each should be used to make a 588 kilo mixture.

amount of Kenyan coffee --- x

amount of Turkish coffee --- 588

11x + 13(588-x) = 12(588)

solve for x and you got it

I have x=58.8

Without even checking the answer by substitution, it sound unreasonable right from the start.

Since the 588 kg sells for $12 and was mixed from a $11 and a $13 source, we would expect the split to be about half way.

11x + 7644 - 13x = 7056
-2x = -588
x = 294

well, what a surprise.

To solve this problem, we can use a system of equations. Let's denote the amount of Kenyan coffee by 'x' in kilograms, and the amount of Turkish coffee by 'y' in kilograms.

According to the problem, the store wants to make a mixture of 588 kilograms, so we have the equation:

x + y = 588 (Equation 1)

The cost of the Kenyan coffee is $11 per kilogram and the cost of the Turkish coffee is $13 per kilogram. The target cost for the mixture is $12 per kilogram. We can set up another equation based on the cost of each coffee:

11x + 13y = 12(588) (Equation 2)

Simplifying Equation 2, we have:

11x + 13y = 7056

Now, we can solve the system of equations (Equation 1 and Equation 2) to find the values of 'x' and 'y' that satisfy both equations.

First, let's rearrange Equation 1 to solve for 'x':

x = 588 - y

Substitute this value of 'x' into Equation 2:

11(588 - y) + 13y = 7056

Distribute 11:

6468 - 11y + 13y = 7056

Combine like terms:

2y = 588

Divide both sides by 2:

y = 294

Now substitute the value of 'y' back into Equation 1:

x + 294 = 588

Subtract 294 from both sides:

x = 294

So, the mixture should contain 294 kilograms of Kenyan coffee and 294 kilograms of Turkish coffee to make a 588-kilogram mixture.