SOLUTION: Please help me with this. I've done similar problems when I was just calculating for how much to invest of two different percentages, but having to calculate the total interest is

Question 1003369: Please help me with this. I've done similar problems when I was just calculating for how much to invest of two different percentages, but having to calculate the total interest is throwing me off:
Wendy was awarded a volleyball scholarship to the University of Michigan, so on graduation her parents gave her the $17,000, they had saved for her college tuition. She opted to invest some money in a privately held company that pays 10% per a year, and evenly split the remaining money between a money market account yielding 2% and a high risk stock that yielded 40%. At the end of the first year she had $19,910 total. How much did she invest in each of the three?
_____ @ 10%
______@ 2%
______@ 40%
Answer by maxitee(11) (Show Source): You can put this solution on YOUR website!
The solution is derive an equation and link two variables together. See below.
Let's call the amount invested for the 10%, A
Let's call the 2%, B and the 40% C.
From the question, B = C.
If she made $19,910 at the end of the first year. We try to sum up all the investments that gave her the returns. Using the above A, B and C. We have.
(10% of A plus A)***THIS IS EVERYTHING SHE GETS FROM THE INVESTMENT, i.e we add her profit(10%) plus her initial investment ******
Applying the above for all other investments we have.

Being that B = C, we can substitute B for C. After doing that and simplifying the above equation we have.

Let's call the above equation (i)
Remember that she invested all her money. Therefore if we sum all the invested amounts, A B and C we will equate it to her initial $17,000

Being that B and C are the same we have a new equation from the above as.

We shall call the above equation (ii).
If we make A subject of formula in equation (ii) we have A = 17,000 - 2B.
So we simply substitute the value of A into equation (i) above. See the result.

From the above B will equate = $5,500
If B is $5,500 C is equally $5,500 which puts A as $6,000.
In conclussion,
$6,000 @ 10%
$5,500 @ 2%
$5,500 @ 40%
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