A coffee distributor needs to mix a (n) Breakfast coffee blend that normally sells for $9.40 per pound with a Gazebo coffee blend that normally sells for $14.10 per pound to create 40 pounds of a coffee that can sell for $10.46 per pound. How many pounds of each kind of coffee should they mix?

Rounding to the next whole number, the coffee distributor should mix 31 pounds of Breakfast coffee blend and 9 pounds of Gazebo coffee blend

Step-by-step explanation:

1. This is the information given to us to answer the question correctly:

Breakfast coffee blend price = $ 9.40

Gazebo coffee blend price = $ 14.10

Mixed coffee blend price = $ 10.46

Pounds of Breakfast coffee blend = x

Pounds of Gazebo coffee blend = 40 - x

2. How many pounds of each kind of coffee should they mix?

Let's answer the question, using the following equation to solve for x:

9.40x + 14.10 (40 - x) = 10.46 (40)

9.4x - 14.1x + 564 = 418.4

- 4.7x = 418.4 - 564

- 4.7x = - 145.6

x = - 145.6/-4.7

x = 30.98 ≅ 31 ⇒ 40 - x = 9

Rounding to the next whole number, the coffee distributor should mix 31 pounds of Breakfast coffee blend and 9 pounds of Gazebo coffee blend