A store mixes Brazilian coffee worth $11 per kilogram and Venezuelan coffee worth $15 per kilogram. The mixture is to sell for $14 per kilogram. Find how much of each is needed to to make a 216-kilogram mixture.
Brazilian coffee needed-
Venezuelan coffee needed-
11B + 15V = 14(B+V)
B+V = 216
11B + 15(216-B) = 14*216
B = 54
V = 162
check:
11*54 + 15*162 = 3024 = 14*216
To find the amount of Brazilian coffee and Venezuelan coffee needed to make a 216-kilogram mixture, we can set up a system of equations based on the given information.
Let's assume that x represents the weight of Brazilian coffee in kilograms and y represents the weight of Venezuelan coffee in kilograms.
Since we want the mixture to sell for $14 per kilogram, the total cost of the mix should be equal to the cost per kilogram multiplied by the total weight. The total cost is given by:
11x + 15y = 14 * 216
Next, we know that the total weight of the mixture is 216 kilograms, so we have:
x + y = 216
Now we have a system of two equations:
11x + 15y = 14 * 216
x + y = 216
We can solve this system of equations to find the amount of Brazilian coffee (x) and Venezuelan coffee (y) needed.
One way to solve this system is by using the method of substitution. Solving the second equation for x, we get:
x = 216 - y
Substituting this value into the first equation:
11(216 - y) + 15y = 14 * 216
Simplifying:
2376 - 11y + 15y = 3024
4y = 648
Dividing both sides by 4:
y = 162
Now we can substitute this value back into the second equation to solve for x:
x + 162 = 216
x = 216 - 162
x = 54
Therefore, we need 54 kilograms of Brazilian coffee and 162 kilograms of Venezuelan coffee to make a 216-kilogram mixture.