SOLUTION: please help with this problem. Suppose you have recieved a total of $1,520 a year in interest from three investments. The interest rates for the investments are 5%, 7%, and 8%.

Question 180221: please help with this problem.

Suppose you have recieved a total of $1,520 a year in interest from three investments. The interest rates for the investments are 5%, 7%, and 8%. The amount is invested at 5% is half of the amount invested at 7%. The amount invested at 7% is $1,500 less than the amount invested at 8% Find the amount of money invested at each rate.

Thank you!
Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
Suppose you have received a total of $1,520 a year in interest from three investments. The interest rates for the investments are 5%, 7%, and 8%. The amount is invested at 5% is half of the amount invested at 7%. The amount invested at 7% is $1,500 less than the amount invested at 8% Find the amount of money invested at each rate.
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Let "x" be amt invested at 5%
Let "y" be amt. invested at 7%
Let "z" be amt. invested at 8%
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Interest Equation: 0.05x + 0.07y + 0.08z = 1520
Quantity Equation: x = (1/2)y
Quantity Equation: y = z - 1500
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Write x and z interms of y:
x = (1/2)y
z = y + 1500
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Substitute into the 1st equation to solve for "y":
0.05((1/2)y) + 0.07y + 0.08(y+1500) = 1520
Multiply thru by 100 to get:
5(1/2)y + 7y + 8(y + 1500) = 152000
(5/2)y + 7y + 8y + 12000 = 152000
(35/2)y = 140000
y = $8000.00 (amt. invested at 7%)
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x = (1/2)y = $4000.00 (amt. invested at 5%)
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z = y + 1500 = $9500 (amt. invested at 8%)
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Cheers,
Stan H.

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