I am flabbergasted. Please help, two variable equations

Question

A coffee distributor needs to mix a(n) Arabian Mocha coffee blend that normally sells for $11.40 per pound with a Breakfast coffee blend that normally sells for $13.80 per pound to create 50 pounds of a coffee that can sell for $11.40 per pound. How many pounds of each kind of coffee should they mix?

Answer:

They must mix

 ______pounds of the Arabian Mocha Blend

 ________pounds of the Breakfast Blend.

Round your answers to the nearest whole number of pounds.

Answer 1

there's a typo somewhere in the problem

the Arabian blend and the final mixture can't be the same price of $11.40

either the Arabian Mocha is < 11.4, or the mixture price is > 11.4, or both

let's say the mixture price for 50 lbs is $12.80 then

13.80B + 11.40A= 12.80(50) and A = 50-B

13.80B+ 11.40(50-B) = 12.80(50)

2.4B = (12.8-11.4)(50) = 1.4(50)

B = 1.4(50)/2.4 = 7(50)/12 = 7(25)/6 = 175/6= 29 1/6 pounds Breakfast Blend

A = 50-26 1/6 =20 5/6 pounds Arabian Mocha Blend

13.8-12.8 = 1

12.8-11.4 = 1.4

1.4/1 = 1.4= B/A = B/(50-B) = 29 1/6/20 5/6 = 175/125= 7/5 = 1.4

B = 50(1.4) - 1.4B

2.4B = 50(1.4)

B = 50(1.4)/2.4) = 50(7/12)= 25(7)/6 = 175/6 = 29 1/6 pound Breakfast Blend

A = 20 1/6 Arabian Mocha Blend