matrix question

Question

A man has $285,000 invested in three properties. One earns 12%, one 10% and one 8%. His annual income from the properties is $27,200 and the amount invested at 8% is twice that invested at 12%.

Answer 1

Investment at 12%. = x $

Investment at  10% = y $

Investment at 8%.   = z $ 

 

x+y+z=285000

 

0.12x +0.10y+ 0.08z =27200

 

z=2x

 

Plug in back in first and second equation

 

3x+y=285000

 

0.28x + 0.10y =27200

 

Multiplying the first equation by 0.1 throughout

 

0.3x +0.1y =28500

 

0.28x +0.1y =27200

 

Subtracting the two

 

0.02 x =1300

 

x=65000

 

z=130000

 

y = 90000