Question 1003369
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.

{{{(10A/100 + A) + (2B/100 + B) + (40C/100 + C) = $19910 }}}
Being that B = C, we can substitute B for C. After doing that and simplifying the above equation we have.

{{{(10A+100A + 2B + 100B + 40B + 100B)/100 = $19910}}}

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

   {{{A + B + C = $17000}}}
Being that B and C are the same we have a new equation from the above as.
{{{A + 2B = $17000}}}
   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.
{{{110(17000-2B) + 242B = 1991000}}}
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%