SOLUTION: Roberto invested some money at 8%, and then invested $2000 more than twice this amount at 12%. His total annual income from the two investments was $4720. How much was invested at

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Question 615830: Roberto invested some money at 8%, and then invested $2000 more than twice this amount at 12%. His total annual income from the two investments was $4720. How much was invested at 12%?
Answer by dragonwalker(73) About Me  (Show Source):
You can put this solution on YOUR website!
Let us say that the amount invested at 8% is a.
A percentage simply represents how many units out of 100 so 8% can be written as 8/100 or 0.08 and 12% can therefore be written as 12/100 or 0.12
so if 'a' is the amount invested at 8% then the amount invested at 12% is:
2a + 2000
(twice 'a' plus 2000)

The gain is the percent of that investment (I assume that it is on the original investment, not accrued).
So the amount returned from the 8% investment is simply 0.08a
The amount returned from the 12% investment is 0.12(2a + 2000)
which can then be simplified by multiplying 0.12 by each part of the formula within the brackets:
(0.12 x 2a) + (0.12 x 2000) = 0.24a + 240
So the total return is that money that comes from both investments:
= 0.08a + 0.24a + 240
= 0.32a + 240
As we know the amount of the return is $4720 (I assume it represents the interest income)
So:
0.32a + 240 = 4720
0.32a = 4720 - 240
0.32a = 4480
so a = 4480/0.32
a = 14000

So now we know 'a' we can figure out the amount invested at 12 % which is
2a + 2000
So:
2a + 2000 = 2*14000 + 2000
= 28000 + 2000
= 30000
The amount invested at 12% is $30000