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.
<u>1st equation
</u>
<em>“A bank wishes to invest a $100, 000 trust fund in three sources”
</em>
x + y + z = 100,000
<u>2nd equation
</u>
<em>“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%”
</em>
<em>
</em>
0.8x + 0.7y + 0.1z = 8,000
3rd equation
<em>“the total amount invested in bonds and certificates of deposit must be triple the amount invested in mortgages”
</em>
<em>
</em>
x+y = 3z
and we have a <em>linear system of 3 equations with 3 unknowns
</em>
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.
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