jmc

Let $x$ be the number of blue marbles and $y$ the number of yellow marbles before I added more. We are given that the ratio of blue to yellow is 4:3, so $\frac{x}{y}=\frac{4}{3}$. Additionally, after we add blue marbles and remove yellow marbles the total number of blue marbles and yellow marbles will be x+5 and y-3 respectively. We're given that at this point the ratio will be $7:3$, so $\frac{x+5}{y-3}=\frac{7}{3}$. Cross multiplying the first equation gives $3x=4y$ and cross multiplying the second gives $3(x+5)=7(y-3)$. Solving two linear equations on two variables is routine; we get the solution $y=12$, $x=16$. Since $x$ represents the number of blue marbles before more were added, the answer to the problem is just $\boxed{16}$.