$4000 was invested at 3% interest.
Solution:
Assume that x and y represent the amount at 3.5% and 3% respectively. So, according to the given statements we get two equations,
[tex]x+y=5000\rightarrow(1)\\\\3x+3.5y=15500\rightarrow(2)[/tex]
On multiplying equation (1) by 30 and equation (2) by 10 we get,
[tex]30 x+30 y=150000\\\\30 x+35 y=155000[/tex]
On solving both the equations we get,
[tex]\Rightarrow5y=5000\rightarrow y=\frac{5000}{5}\rightarrow y=1000\rightarrow(3)[/tex]
On substituting (3) in (1) we get,
[tex]\Rightarrow x+1000=5000\rightarrow x=5000-1000\rightarrow x=4000[/tex]
Therefore, $4000 was invested at 3% interest and $1000 was invested at 3.5% interest.
