Tea Mixing Cost Calculation

Tea mixing is a common practice done by dealers to create different blends of tea with varying flavors and qualities. In this scenario, let's assume that the dealer has a stock of different types of tea and wants to create a blend that costs $6.92 per unit.

To calculate the cost of the tea blend, we need to consider the cost of each type of tea used in the mix and their respective quantities.

Gather Information
First, we need to gather all the necessary information about the types of tea available and their costs. Let's say the dealer has three types of tea in stock:

1. Type A Tea: $4.00 per unit
2. Type B Tea: $6.50 per unit
3. Type C Tea: $8.20 per unit

Determine the Ratio
To create a tea blend that costs $6.92 per unit, we need to determine the ratio of each type of tea used in the mix. This can be done by finding a combination of the three teas that will result in the desired cost per unit.

Calculate the Ratio
Let's assume we use x units of Type A Tea, y units of Type B Tea, and z units of Type C Tea in the blend. We can set up the following equation to calculate the ratio:

4x + 6.5y + 8.2z = 6.92(x + y + z)

Simplifying the equation:

4x + 6.5y + 8.2z = 6.92x + 6.92y + 6.92z

Rearranging the terms:

4x - 6.92x + 6.5y - 6.92y + 8.2z - 6.92z = 0

-2.92x - 0.42y + 1.28z = 0

Solve the Equation
To find the values of x, y, and z, we need to solve the equation. This can be done using various methods such as substitution, elimination, or matrix algebra. Once the values of x, y, and z are determined, we can calculate the quantities of each type of tea needed in the blend.

Calculate the Quantities
Using the values of x, y, and z obtained from solving the equation, we can calculate the quantities of each type of tea needed in the blend. The quantities can be expressed as percentages or ratios based on the total quantity of the blend.

Verify the Cost
Finally, we can verify that the cost of the tea blend is indeed $6.92 per unit by multiplying the quantities of each type of tea by their respective costs and summing them up. The total cost should equal $6.92.

Conclusion
In conclusion, mixing tea involves determining the ratio of different types of tea to create a blend with a desired cost per unit. By solving an equation and calculating the quantities of each type of tea, the dealer can create a tea blend that costs $6.92 per unit.