Solve the problem. A $98,000 trust is to be invested in bonds paying 7%, CDs paying 5%, and mortgages paying 10%. The bond and CD investment together must equal the mortgage investment. To earn a $7550 annual income from the investments, how much should the bank invest in bonds?

bonds = $10000

CD = $39000

Mortgage = $49000

Step-by-step explanation:

Let x represent the amount that should be invested in the bond.

Let y represent the amount that should be invested in the CD.

Let z represent the amount that should be invested in the mortgage.

A $98,000 trust is to be invested in bonds paying 7%, CDs paying 5%, and mortgages paying 10%. It means that

x + y + z = 98000 - - - - - - -1

The bond and CD investment together must equal the mortgage investment. It means that

z = x + y

To earn a $7550 annual income from the investments, it means that

0.07x + 0.05y + 0.1z = 7550- - - - -- 2

Substituting z = x + y into equation 1 and equation 2, it becomes

x + y + x + y = 98000

2x + 2y = 98000

Dividing through by 2,

x + y = 49000

x = 49000 - y - - - - - - -3

0.07x + 0.05y + 0.1(x + y) = 7550

0.07x + 0.05y + 0.1x + 0.1y = 7550

0.17x + 0.15y = 7550- - - - - - - - -4

Substituting equation 3 into equation 4, it becomes

0.17(49000 - y) + 0.15y = 7550

8330 - 0.17y + 0.15y = 7550

- 0.17y + 0.15y = 7550 - 8330

- 0.02y = - 780

y = - 780/-0.02

y = 39000

x = 49000 - y = 49000 - 39000

x = 10000

Substituting x = 10000 and y = 39000 into z = x + y 1, it becomes

z = 10000 + 39000 = 49000