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Question 76647: Will someome please help me solve, someone was kind enough to show me how to do this with two numbers will someone please help me with this one? The problem is A stockbroker has money in three accounts. The interest rates on the three accounts are 4%, 6%, and 12%. If she has twice as much money invested at 6% as she has invested at 4%, three times as much at 12% as she has at 4%, and the total interest for the year is $260, how much is invested at each rate? (Hint: Let x = the amount invested at 4%.)
invested at 4%
invested at 6%
invested at 12%
Please Help Me
Thank You,
Sabrina
Answer by bucky(2189)   (Show Source):
You can put this solution on YOUR website! Let x equal the amount she has invested at 4%. According to the problem, the amount she has
invested at 6% is twice the amount she has invested at 6%. So the amount she has invested at
6% is 2*x. Also according to the problem, the amount she has invested at 12% is 3 times the
amount she has invested at 4%. So she has 3*x invested at 12%.
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The amount of interest she makes is 4% (or 0.04) times the amount invested at 4% which is x.
So the interest she makes at 4% is 0.04*x.
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The amount of interest she makes is 6% (or 0.06) times the amount invested at 6% which is 2*x.
So the interest she makes at 6% is 0.06*2*x or 0.12x.
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The amount of interest she makes is 12% (or 0.12) times the amount invested at 12% which is 3*x.
So the interest she makes at 12% is 0.12*3*x which multiplies out to 0.36*x.
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The total interest she makes is the sum of these three amounts or:
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0.04*x + 0.12*x + 0.36*x
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And these three terms combine to 0.52*x which is the total interest. But the problem tells
you that the total interest is $260. Therefore, we can set these two amounts equal and in
equation form this is:
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0.52*x = 260
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Solve for x by dividing both sides by 0.52 and you get:
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x = 260/0.52 = $500.
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Since x was the amount invested at 4% we now know that amount ... $500.
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Twice as much was invested at 6%, so the amount invested at 6% is $1000.
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And three times as much was invested at 12% ... so $1500 is invested at 12%.
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And 4% of $500 is $20; 6% of $1000 is $60; and 12% of $1500 is $180. So the total interest
is $20 + $60 + $180 = $260. Yep, that checks out as being what the problem said it should
be, so we can be pretty confident in our answers.
.
Hope this work supplements answer 54967 to your problem #76645 and gives you a pretty good
idea by now of how to work this type of a problem.
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