Answer
She invested 500 dollars at 4%.
She invested 1000 dollars at 5%.
She invested 1500 dollars at 6%.
Work Step by Step
Let X represent the sum of money invested at 4%.
She earned 4% $\times$ X = 0.04X from this investment.
She invested twice that sum at 5%. So, she invested 2X at 5%.
She earned 5% $\times$ 2X = 0.1X from this investment.
She invested three times that sum at 6%. So, she invested 3X at 6%.
She earned 6% $\times$ 3X = 0.18X from this investment.
Her total interest from all three investments was 160 dollars.
We can set up the following equation:
0.04X + 0.1X + 0.18X = 160
0.32X = 160
Divide both sides by 0.32:
X = 500
She invested 500 dollars at 4%.
She invested twice that sum, or 500$\times$2 = 1000 dollars at 5%.
She invested three times that sum, or 500$\times$ 3 = 1500 dollars at 6%.
