Find the system of equations to model the problem and find i

Find the system of equations to model the problem and find its solution A $124,000 trust is to be invested in bonds paying 9%, CDs paying 8%, and mortgages paying 10%. The sum of the amount invested in bonds and the amount invested in CDs must equal the mortgage investment. To earn an $11, 400 annual income from the investments, how much should the bank invest in each? Let x represent the amount invested in bonds, y the amount invested in CDs, and z the amount invested in mortgages.

Solution

equations are

x+y+z=124000

x+y=z

0.09x+0.08y+0.10z=11400

=>9x+8y+10z=1140000

x+y+z=124000,x+y=z

=>z+z =124000

=>2z=124000

=>z=62000

x+y=z, z=62000

=>x+y =62000

z=62000,9x+8y+10z=1140000

=>9x+8y+620000=1140000

=>9x+8y=520000

x+y =62000 =>8x+8y =496000

9x+8y -8x-8y=520000-496000

=>x=24000

x+y =62000 ,x=24000

=>24000+y =62000

=>y=38000

bank should invest 24000$ in bonds , 38000$ in CDs ,62000$ in mortgages