A man has 446500 invested in three properties One earns 12 o

A man has $446,500 invested in three properties. One earns 12%, one 10%, and one 896 His annual income from the properties is $42,750 and the amount invested at 8% is twice that invested at 12%. What is the annual income from each property? 5. a. S53,580; $4,465; s35,720 b. $11,400; $16,150; S15,200 c. $14,592; S 10,830; $17,328 d. S10,545; $17,575; $18,287.5 e. $16,872; $7,030; $18,848

Solution

let amount invested in 12% one =x , 10% one =y , 8% one =z

x+y+z =446500

annual income =(12/100)x+(10/100)y+(8/100)z=42750

12x+10y+8z=4275000

amount investes in 8% one is twice thant of 12% one

z=2x

z=2x ,12x+10y+8z=4275000 =>28x+10y=4275000

z=2x ,x+y+z =446500 =>3x+y=446500 =>30x+10y=4465000

30x+10y-28x-10y=4465000-4275000

2x=190000

x =95000

z=2x

z=190000

x+y+z =446500

y=446500-190000-95000

y=161500

income from 12% one =(12/100)*95000 =11400

income from 10% one =(10/100)*161500 =16150

income from 8% one =(8/100)*190000 =15200