Two varieties of herbal tea,
one cost $4.00 per kilogram
other cost $5.00 per kilogram.
How many kilograms of each type are needed to make 20kg of a blend worth $4.60 per kilogram?
To determine how many kilograms of each type of herbal tea are needed, we can set up a system of equations based on the given information.
Let's assume x represents the number of kilograms of the $4.00 per kilogram tea, and y represents the number of kilograms of the $5.00 per kilogram tea.
1) The total weight of the blend is 20 kg, so we have the equation:
x + y = 20
2) The total cost of the blend is $4.60 per kilogram, so the value of the $4.00 per kilogram tea plus the value of the $5.00 per kilogram tea should equal the total cost. The equation can be written as:
4x + 5y = 4.60 * 20
Now we have a system of two equations:
x + y = 20
4x + 5y = 92
To solve this system, we can use the method of substitution or elimination.
Let's use the substitution method here.
From the first equation, we can express x in terms of y:
x = 20 - y
Substitute x in the second equation with 20 - y:
4(20 - y) + 5y = 92
80 - 4y + 5y = 92
80 + y = 92
y = 92 - 80
y = 12
Now substitute the value of y back into the first equation to solve for x:
x + 12 = 20
x = 20 - 12
x = 8
Therefore, you need 8 kilograms of the $4.00 per kilogram tea and 12 kilograms of the $5.00 per kilogram tea to make a 20 kg blend worth $4.60 per kilogram.