Question 109232This question is from textbook College Algebra In Context
: A trust account manager has $500,000 to be invested in three different accounts. The accounts pay 8%, 10%, and 14%, respectively, and the goal is to earn $49,000 with the amount invested at 8% equal to the sum of the other two investments. To accomplish this, assume that x dollars are invested at 8%, y dollars are invested at 10%, and z dollars are invested at 14%.
a. Write an equation that describes the sum of money in the three investments.
b. Write an equation that describes the total amount of money earned by the three investments.
c. Write an equation that describes the relationship among the three investments.
d. solve the system of equations to find how much should be invested in each accournt to satisfy the conditions.
This question is from textbook College Algebra In Context
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! A trust account manager has $500,000 to be invested in three different accounts. The accounts pay 8%, 10%, and 14%, respectively, and the goal is to earn $49,000 with the amount invested at 8% equal to the sum of the other two investments. To accomplish this, assume that x dollars are invested at 8%, y dollars are invested at 10%, and z dollars are invested at 14%.
a. Write an equation that describes the sum of money in the three investments.
x+y+z = 500,000
b. Write an equation that describes the total amount of money earned by the three investments.
0.08x+0.10y+0.14z = 49000
c. Write an equation that describes the relationship among the three investments.
x-y-z=0
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d. solve the system of equations to find how much should be invested in each accournt to satisfy the conditions.
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I used the TI-83 Matrix capability to find
x = 250,000
y = 150,000
z = 100,000
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Cheers,
Stan H.
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