Question 76647
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.
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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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