Question

A coffee distributor needs to mix a(n) Kenya coffee blend that normally sells for $11.60 per pound with a Queen City coffee blend that normally sells for $14.30 per pound to create 70 pounds of a coffee that can sell for $13.91 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 Kenya coffee blend.
Equation:

B) Answer: They must mix
pounds of the Kenya Blend
pounds of the Queen City Blend.

Answer 1

Answer: They must mix 10

pounds of the Kenya Blend and 60

pounds of the Queen City Blend.

Step-by-step explanation:

Let x represent the the quantity of Kenya coffee blend.

Let y represent the the quantity of Queen City coffee blend.

The quantity o coffee to be created is 70 pounds. This means that

x + y = 70

The coffee distributor needs to mix a(n) Kenya coffee blend that normally sells for $11.60 per pound with a Queen City coffee blend that normally sells for $14.30 per pound to create 70 pounds of a coffee that can sell for $13.91 per pound. The total cost of the mixture is

70 × 13.91 = $973.7

The expression would be

11.6x + 14.3y = 973.7 - - - - - - - - - 1

Substituting x = 70 - y into equation 1, it becomes

11.6(70 - y) + 14.3y = 973.7

812 - 11.6y + 14.3y = 973.7

- 11.6y + 14.3y = 973.7 - 812

2.7y = 161.7

y = 161.7/2.7

y = 59.88

Approximately 60 pounds.

x = 70 - y = 70 - 60

x = 10 pounds