Let's say Carla invested amount $x at 16%. Then she invested amount ($23,000-x) at 15%. Her yield is

3500 = x*16% + (23000-x)*15% (write an equation expressing the problem facts)

3500 = x*16% + 23000*15% - x*15% (use the distributive property)

3500 = x*1% + 3450 (collect terms, perform the 15% calculation)

50 = x*1% (subtract 3450 from both sides)

50/1% = x (divide both sides by 1%)

5000 = x (perform the 1% calculation)

Carla invested $5000 at 16% interest.

3500 = x*16% + (23000-x)*15% (write an equation expressing the problem facts)

3500 = x*16% + 23000*15% - x*15% (use the distributive property)

3500 = x*1% + 3450 (collect terms, perform the 15% calculation)

50 = x*1% (subtract 3450 from both sides)

50/1% = x (divide both sides by 1%)

5000 = x (perform the 1% calculation)

Carla invested $5000 at 16% interest.