Help please with high school Alg 2 homework

Question

A $62,000 trust is to be invested in bonds paying 9%, CDs paying 8%, and mortgages paying 10%. The bond and CD investment together must equal the mortgage investment. To earn a $5710 annual income from the investments, how much should the bank invest in bonds?

Answer 1

This will involve solving a system of equations, 3 equations and 3 unknowns. First, define the variables.

Let x = amount invested in bonds

Let y = amount invested in CDs

Let z = amount invested in mortgages

The first equation is around the total amount invested

x+y+z=62000

The next equation is around the amount of interest earned.

0.09x+0.08y+0.10z=5710

The last equation comes from this sentence. The bond and CD investment together must equal the mortgage investment.

x+y=z

Can you solve this system of equations?