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
