An executive invests $27,000, some at 8% and the rest at 7% annual interest. if he receives an annual return of $2,050, how much is invested at each rate

8%X + 7%(27000-X) = 2050
.08X + 1890 + .07X = 2050
.15X = 160
X = $1067.67

Let x be the amount invested at 8%
the remaining amount (27,000 - x) was invested at 7%. After one year 
$x yielded an interest A₁  OR A₁ = x(0.08)
The remained yielded an interest of A₂ = (27000 - x) (8%)
A₁   =   x(0.08)
A₂   =   (27000 - x) (8%)
     
A₁+A₂ = x(0.08) + (27000 - x) (8%)

2050 = x(0.08) + (27000 - x) (8%)

2050 = 0.08x - 0.07x +1890
2050 - 1890 = 0.01x

x = 160/0.01 = $16,000 @ 8% and $11,000 @ 7%