Step-by-step explanation:
a lot of typos in the problem description.
I assume the price of the mix is 1:1 related to the prices of the individual types of coffee.
so, from what I understood we can define
x = pounds of the first type of coffee.
y = pounds of the second type of coffee.
x + y = 21 pounds
1.4x + 2.95y = 2.6(x + y) = 2.6×21 = $54.60
in the second equation we have to bring the given "$2.60 per pound" to the total price, which is $2.60 times the total amount of pounds (which is 21).
from the first equation we get
x = 21 - y
and that we use in the second equation
1.4×(21 - y) + 2.95y = 54.6
29.4 - 1.4y + 2.95y = 54.6
1.55y = 25.2
y = 25.2 / 1.55 = 16.25806452... ≈ 16.26 pounds
x = 21 - y = 4.741935484... ≈ 4.74 pounds
so, he should mix 4.74 pounds of the first (cheaper) type and 16.26 pounds of the second (expensive) type.
