The vector a = (5, 7) and b = (m, 3) such that 3a + 2b = (n, 26). Find the values of m and n.

Multiply each component of vector $b$ by 2:

$$2 \begin{pmatrix} m \\ -3 \end{pmatrix} = \begin{pmatrix} 2m \\ 2 \times (-3) \end{pmatrix} = \begin{pmatrix} 2m \\ -6 \end{pmatrix}$$

Substitute the result back into the equation and add the corresponding components:

$$\begin{pmatrix} 2 \\ 7 \end{pmatrix} + \begin{pmatrix} 2m \\ -6 \end{pmatrix} = \begin{pmatrix} 5 \\ n \end{pmatrix}$$ $$\begin{pmatrix} 2 + 2m \\ 7 + (-6) \end{pmatrix} = \begin{pmatrix} 5 \\ n \end{pmatrix}$$ $$\begin{pmatrix} 2 + 2m \\ 1 \end{pmatrix} = \begin{pmatrix} 5 \\ n \end{pmatrix}$$

For the vectors to be equal, their x-components must be equal and their y-components must be equal.
From the x-components:

$$2 + 2m = 5$$

From the y-components:

$$1 = n$$

From the y-components, we directly get:

$$n = 1$$

From the x-components:

$$2m = 5 - 2$$ $$2m = 3$$ $$m = \frac{3}{2}$$

The values are $\boxed{m = \frac{3}{2}, n = 1}$.