Question

The Comfort Coffee Company wants to mix 20 pounds of their Smooth blend worth a $6 pound with their Special blend worth $6.50 a pound in order to create a new blend of coffee worth a pound. How many pounds of the Special blend should be added to the Smooth​ blend?

Answer 1

Answer: Let's call the number of pounds of Special blend added to the Smooth blend "x".

Since the price of the new blend is $6.00 a pound, the weighted average price per pound of coffee must also be $6.00.

To find the weighted average, we need to multiply the price of each blend by the number of pounds of each blend, and then divide by the total number of pounds of coffee.

This means that no Special blend should be added to the Smooth blend. If the goal is to create a new blend with a price of $6.00 per pound, it is not possible to achieve this goal by mixing the two blends.

Explanation:

Here's the equation:

$6.00 = [20 * $6.00 + x * $6.50] / (20 + x)

Expanding the equation:

$6.00 = $120.00 + $6.50x / 20 + x

$6.00 = $120.00 / 20 + $6.50x / 20 + x

$6.00 * 20 + $6.50x = $120.00 + $6.50x

$120.00 + $6.50x = $120.00

$6.50x = 0

So x = 0.

This means that no Special blend should be added to the Smooth blend. If the goal is to create a new blend with a price of $6.00 per pound, it is not possible to achieve this goal by mixing the two blends.