Answer:
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.
