A store mixes kenyan coffee worht $12 per kilogram and turkish coffee worth $16 per kilogram the mixture is to sell for $14 per kilogram how much of each should be used to make a 348-kilogram mixture?
348/2 for each
To solve this problem, let's use a system of equations.
Let x represent the amount of Kenyan coffee in kilograms, and y represent the amount of Turkish coffee in kilograms.
We have two equations based on the given information:
Equation 1: x + y = 348 (since the total amount of mixture is 348 kilograms)
Equation 2: (12x + 16y) / 348 = 14 (since the cost of the mixture is $14 per kilogram)
Now, let's solve this system of equations.
From Equation 1, we can express x in terms of y: x = 348 - y.
Substituting x in Equation 2, we get: (12(348 - y) + 16y) / 348 = 14.
Simplify the equation: (4176 - 12y + 16y) / 348 = 14.
Combine like terms: (4176 + 4y) / 348 = 14.
Cross-multiply: 4176 + 4y = 14 * 348.
Simplify further: 4176 + 4y = 4872.
Subtract 4176 from both sides: 4y = 4872 - 4176.
Simplify: 4y = 696.
Divide both sides by 4: y = 174.
We found that y = 174. Now, substitute this value of y into Equation 1 to find x.
x + 174 = 348.
x = 348 - 174.
x = 174.
Therefore, the mixture should consist of 174 kilograms of Kenyan coffee and 174 kilograms of Turkish coffee.