Answer:
23 pounds of the Gualtemala Antigua Blend and 37 pounds of the Tanzanian Blend
Step-by-step explanation:
you need to make a system of equations to solve this.
First lets make x be the pounds of Gualtemala Antigua coffee blend and y the pounds of Tanzanian coffee blend
we know we need 60 pounds total so first equation is
x+y=60
Next we will make an equation based on the money information
10.30x + 13.80y = 12.46(60)
10.30x + 13.80y = 747.60
So our system of equations is
x + y = 60
10.30x + 13.80y = 747.60
I will solve this by using substitution. first rewrite x+y=60 to y=60-x
now i can substitute that into the other equation for y and solve for x
10.30x + 13.80(60-x) = 747.60
10.30x + 828 -13.80x = 747.60
-3.5x + 828 = 747.60
-3.5x = -80.4
x = 23 (rounded from 22.9714 since they requested that)
now I can use this solution to solve for y by plugging into one of the original equations
x + y =60
23 + y =60
y = 37
Finally we can say that they must mix 23 pounds of the Gualtemala Antigua Blend and 37 pounds of the Tanzanian Blend.
(using 
)
so we can replace the sin²x in the LHS expression as follows
which is the RHS.