Answer:
 for 8% investment = $110000
 for 12% investment = $55000
 for 10% investment =  $80000
annual income for each property is 
x amount for 8% investment = $8800
y amount for 12% investment = $6600
z amount for 10% investment = $8000
Explanation:
Given data 
investment = $245000
rate 1 = 12%
rate 2 = 10%
rate 3 = 8%
annual income = $23400
rate = 8%  twice that invested at 12%
to find out 
invested in each property and  the annual income from each property
solution
let us consider x amount for 8% investment
and consider y amount for 12% investment
and consider z amount for 10% investment
from question we say,  8% is twice that invested at 12%
x = 2y      ........1
and 
x + y + z = 245000      .............2
put 1 in equation 2 
2y + y + z = 245000  
z = 245000 - 3y            ...................3
and we can say that
0.08x + 0.12y + 0.10z = 23400              ...........................4
put equation 1 and 3 in 4
0.08(2y) + 0.12y + 0.10( 245000 - 3y ) = 23400
0.16y + 0.12y - 0.3y = -1100
0.02y = 1100
y = $55000
so x = 2(y) = 2(5500) = $110000
and z = 245000 - 3(55000) = $80000
so annual income for each property is 
x amount for 8% investment = 0.08 × 110000 = $8800
y amount for 12% investment = 0.12 × 55000 = $6600
z amount for 10% investment = 0.10 × 80000 = $8000