Ruth has $15000 to invest. she invests some of her money earned 7% simple interest and the rest earned 5.5%. if the total interest she earned in one year has $952.50 , how much was invested at each interest rate?

Invested at 7%:  s
Invested at 5.5%:  f
Then s+f=$15000, or f= $15000-s

Then add together the 2 interest amounts:

i = s(0.07) at 7%
i = f(0.055) at 5.5%

Then 0.07s + (15000-s)(0.055) = $952.50

Solve this for s, the amt. invested at 7%:

0.07s + 15000(0.055) - 0.055s = 952.50
Combining the s terms, 

0.015s = 952.50-825
               
                 952.50-825 
Then s = = 8500
                        0.015

Ruth invests $8500 at 7% and $6500 at 5.5%.