A coffee distributor plans to mix some Breakfast coffee that normally sells for $9.40
per pound with some House coffee that normally sells for
$12.80 per pound to create 30 pounds of a new coffee blend that can sell
for $10.99 per pound.
How many pounds of each kind of coffee should they mix?

pounds of Breakfast coffee.
pounds of House coffee.
Round your answers to the nearest whole number of pounds.
HELP ASAP

16 pounds of Breakfast coffee.

14 pounds of House coffee.

Step-by-step explanation:

Let us represent pounds of Breakfast coffee = a

pounds of House coffee = b

So,

a + b = 30 Equation 1

We are told that coffee distributor plans to mix some Breakfast coffee that normally sells for $9.40 per pound with some House coffee that normally sells for $12.80 per pound to create 30 pounds of a new coffee blend that can sell for $10.99 per pound.

So we create the equation:

9.40a + 12.80b / 30 = 10.99

Cross multiply

9.40a + 12.80b = 10.99 × 30

9.40a + 12.80b = 329.7Equation 2

Hence,

a + b = 30 Equation 1

9.40a + 12.80b = 329.7Equation 2

a = 30 - b Equation 3

Substitute 30 - b for a in Equation 2

9.40(30 - b) + 12.80b = 329.7

282 - 9.40b + 12.80b = 329.7

- 9.40b + 12.80b = 329.7 - 282

3.4b =47.7

b = 14.029411765 pounds

To the nearest whole number, pounds of house coffee = 14 pounds

To find a , we would substitute 14 pounds for b in equation 1

a + b = 30 pounds

a + 14 = 30

a = 30 - 14

a = 16 pounds.

Breakfast coffee = 16 pounds.

Therefore, the pounds of each coffee that they should mix is

16 pounds of Breakfast coffee and 14 pounds of House coffee.

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