Answer:
16 pounds of Breakfast coffee.
14 pounds of House coffee.
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 = 329.7..........Equation 2
Hence,
a + b = 30 ......... Equation 1
9.40a + 12.80b = 329.7..........Equation 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.