A bank wishes to invest a $100, 000 trust fund in three sources: bonds paying 8%; certificates of deposit paying 7%; and first mortgages paying 10%. The bank wishes to realize an $8, 000, annual income from the investment. A condition of the trust is that the total amount invested in bonds and certificates of deposit must be triple the amount invested in mortgages. How much should the bank invest in each possible category?

It is not possible to make the investment under the given conditions.

Step-by-step explanation:

Let x, y and z be the amounts invested in bonds, certificates of deposit and mortgages respectively.

1st equation

"A bank wishes to invest a $100, 000 trust fund in three sources"

x + y + z = 100,000

2nd equation

"The bank wishes to realize an $8, 000, annual income from the investment and bonds paying 8%; certificates of deposit paying 7%; and first mortgages paying 10%"

0.8x + 0.7y + 0.1z = 8,000

3rd equation

"the total amount invested in bonds and certificates of deposit must be triple the amount invested in mortgages"

x+y = 3z

and we have a linear system of 3 equations with 3 unknowns

x + y + z = 100,000

0.8x + 0.7y + 0.1z = 8,000

x + y - 3z = 0

This system has a unique solution given by

x = - 470,000

y = 545,000

z = 25,000

Since x is negative, we deduct there is no way to do such an investment.