The total wage, W, earned by a worker in a week is given by the formula W = 15h + 50, where W is the total wage in Ghana cedis and h is the number of hours worked. Find the wage for 20 hours, 35 hours

$$
W = 15(20) + 50
$$

$$
W = 300 + 50
$$
$$
W = 350
$$
The wage for 20 hours is $\boxed{\text{GHC 350.00}}$.

$$
W = 15(35) + 50
$$

$$
W = 525 + 50
$$
$$
W = 575
$$
The wage for 35 hours of work is $\boxed{\text{GHC 575.00}}$.

$$
500 = 15h + 50
$$

$$
500 - 50 = 15h
$$
$$
450 = 15h
$$

$$
h = \frac{450}{15}
$$
$$
h = 30
$$
It will take $\boxed{\text{30 hours}}$ for the wage to reach GHC 500.00.

$$
2\mathbf{p} = 2 \begin{pmatrix} 6 \\ -2 \end{pmatrix} = \begin{pmatrix} 2 \times 6 \\ 2 \times -2 \end{pmatrix} = \begin{pmatrix} 12 \\ -4 \end{pmatrix}
$$

$$
2\mathbf{p} - \mathbf{q} = \begin{pmatrix} 12 \\ -4 \end{pmatrix} - \begin{pmatrix} -4 \\ 3 \end{pmatrix}
$$
$$
2\mathbf{p} - \mathbf{q} = \begin{pmatrix} 12 - (-4) \\ -4 - 3 \end{pmatrix}
$$
$$
2\mathbf{p} - \mathbf{q} = \begin{pmatrix} 12 + 4 \\ -7 \end{pmatrix}
$$
$$
2\mathbf{p} - \mathbf{q} = \boxed{\begin{pmatrix} 16 \\ -7 \end{pmatrix}}
$$

For $\mathbf{p} = \begin{pmatrix} 6 \\ -2 \end{pmatrix}$, $x=6$ and $y=-2$.
$$
||\mathbf{p}|| = \sqrt{6^2 + (-2)^2}
$$

$$
||\mathbf{p}|| = \sqrt{36 + 4}
$$

$$
||\mathbf{p}|| = \sqrt{40}
$$
$$
||\mathbf{p}|| = \sqrt{4 \times 10} = 2\sqrt{10}
$$
The magnitude of $\mathbf{p}$ is $\boxed{2\sqrt{10}}$.