Q. 56 - Precalculus Enhanced with Graphing Utilities

Question

A coffee distributor is blending a new coffee that will cost $\backslash (6.90$ per pound. It will consist of a blend of $\backslash )6.00$ per pound coffee and$\$9.00$  per pound coffee. What amounts of each type of coffee should be mixed to achieve the desired blend?

[Hint: Assume that the weight of the blended coffee is
$100$ pounds.]

Step-by-Step Solution

Answer

The desired blend can be achieved by mixing $70$ pound of $\$6.00$ with $30$ pound of $\$9.00$.

Step 1. Given

The coffee consist of a blend of $\$6$ per pound and $\$9$ per pound.

A coffee distributor is blending a new coffee that will cost $\$6.90$

Weight of the blended coffee is $100$

Step 2. Giving variables.

Let $x$ denote the amount of coffee needed in $\$6$ coffee and $y$ denotes the amount of coffee needed in $\$9$ coffee.

The total amount of coffee is $100$

$$\begin{gathered} x+y=100 \\ y=100-x \end{gathered}$$

Then the equation will be,

$$\begin{gathered} 6x+9y=6.90\left(100\right) \\ 6x+9(100-x)=6.90\left(100\right) \end{gathered}$$

Step 3. Solve the equation.

Solve the above equation,

$$\begin{gathered} 6x+9(100-x)=6.90\left(100\right) \\ 6x+900-9x=690 \\ 9x-6x=900-690 \\ 3x=210 \\ x=70 \end{gathered}$$

Step 4. Find the other quantity of coffee blend.

Since

 $$\begin{gathered} y=100-x \\ =100-70 \\ =30 \end{gathered}$$

Thus $70$ pound is needed in $\$6.00$ coffee and $30$ pound is needed in $\$9.00$ coffee