Question

A coffee distributor needs to mix a(n) Terraza coffee blend that normally sells for $8.00 per pound with a Ethiopian coffee blend that normally sells for $13.70 per pound to create 30 pounds of a coffee that can sell for $8.57 per pound. How many pounds of each kind of coffee should they mix? A) Write an equation using the information as it is given above that can be solved to answer the question. Use x as your variable to represent the quantity of Terraza coffee blend. Equation: B) Answer: They must mix pounds of the Terraza Blend pounds of the Ethiopian Blend. Round your answers to the nearest whole number of pounds.

Answer 1

Assign variables to the amount of each type of coffee.

`\begin{gathered} x=\text{Terraza coffee blend} \\ y=\text{Ethiopian coffee blend} \end{gathered}`

The table below indicates the cost, weight, and the product of the cost and the weight of each type of coffee. Note that since the weight of the final coffee is 30, the weight of the Ethiopian coffee "y" will be the difference between 30 and x.

To obtain an equation, add the products of the two types of coffee and then equate it to the product obtained for the final coffee.

Thus, we have the following:

`8x+13.7(30-x)=8.57(30)`

To find the weight of each type of coffee, solve for the value of x. Simplify both sides of the equation.

`\begin{gathered} 8x+411-13.7x=257.1 \\ -5.7x+411=257.1 \end{gathered}`

To isolate the variable term, subtract both sides of the equation by 411.

`\begin{gathered} -5.7x=257.1-411 \\ -5.7x=-153.9 \end{gathered}`

To obtain the value of x, divide both sides of the equation by -5.7.

`\begin{gathered} (-5.7x)/(-5.7)=(-153.9)/(-5.7) \\ x=27 \end{gathered}`

Thus, the weight of the Terraza coffee is 27 pounds.

To obtain the weight of the Ethiopian coffee, subtract the total weight by the obtained weight of the Terraza coffee.

`\begin{gathered} y=30-x \\ y=30-27 \\ y=3 \end{gathered}`

Thus, the weight of Ethiopian coffee is 3 pounds.

Final answer:

`\begin{gathered} PartA\colon8x+13.7(30-x)=8.57(30) \\ PartB\colon \\ \text{Terraza coffee}\colon27pounds \\ \text{Ethipian coffee}\colon3pounds \end{gathered}`