Chapter 11, Problem 101RE

To determine

What amounts of each type of coffee should be mixed to achieve the desired blend?

Answer to Problem 101RE

  $\boxed{30pounds,70pounds}$

Explanation of Solution

Given information:

A coffee distributor is blending a new coffee that will cost $\$6.90$ per pound. It will consist of blend of $\$6.00$ 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.]

Calculation:

Consider each blend of coffee be $x,y$ now the weight of blended coffee is 100 pounds.

Now,

  $\begin{array}{l}x+y=100\\ x=100-y\\ 6x+9y=6.90\times 100\\ 6x+9y=690\\ put,x=100-y\\ 6\left(100-y\right)+9y=690\\ 600-6y+9y=690\\ 3y=690-600\\ y=90/3\\ y=30\end{array}$

Now put $y=30$ in $x=100-y$ we get,

  $\begin{array}{l}x=100-30\\ x=70\end{array}$

Hence, the amount of $\$6.00$ per pound coffee and $\$9.00$ per pound coffee is $\boxed{30pounds,70pounds}$