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Question 799410: Last year Miley Cyrus earned a total of $784 in interest from 2 investments.
Suppose that she invested a total of $28,000, part of it at 2.4% and the rest at 3.1%.How much did she initially invest at each rate.
Answer by DrBeeee(684)   (Show Source):
You can put this solution on YOUR website! Let a = the amount invested at 2.4%
Let b = the amount invested at 3.1%
The total amount invested is given by
(1) a + b = 28,000
The total interest earned is given by
(2) 0.024*a + 0.031*b = 784
Solve (1) for a and substitute it into (2) to get
(3) 0.024*(28000 - b) + 0.031*b = 784 or
(4) 672 - 0.024*b + 0.031*b = 784 or
(5) 0.007*b = 784 - 672 or
(6) 0.007*b = 112
(7) b = 112/0.007 or
(8) b = 16000
Now use (1) to find a as
(9) a + 16000 = 28000 or
(10) a = 28000 - 16000 or
(11) a = 12000
Always check your answer. Use (2) to do it.
Is ( 0.024*12000 + 0.031*16000 = 784)?
Is (288 + 496 = 784)?
Is (784 = 784)? Yes
Answer: Miley Cyrus initially invested $12,000 @ 2.4% and $16,000 @ 3.1%.
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