To solve this system of equations, we can first simplify the second equation:

(0.5x + 0.5y) * 102 = 91.5
Dividing by 102 on both sides:
0.5x + 0.5y = 0.8970588

Now we can use the first equation to express one variable in terms of the other. Let's solve for y:

27x + 277y = 85.8
277y = 85.8 - 27x
y = (85.8 - 27x) / 277

Now substitute this expression for y into the simplified second equation:

0.5x + 0.5 * (85.8 - 27x) / 277 = 0.8970588
0.5x + 0.429805 = 0.8970588
0.5x = 0.4672538
x = 0.9345076

Now substitute this value of x back into the expression for y to find its value:

y = (85.8 - 27 * 0.9345076) / 277
y ≈ 0.1044221

Therefore, the solution to the system of equations is x ≈ 0.9345076 and y ≈ 0.1044221.