Translate the following sentences into algebraic equations: 1 The product of b and 5 is 125. 2 The value of b is half the value of c. 3 The difference between k and 9 is 4.

Here are the algebraic equations for the given sentences:

4.1
The product of $b$ and 5 is 125.

$$\boxed{5b = 125}$$

4.2
The value of $b$ is half the value of $c$.

$$\boxed{b = \frac{1}{2}c} \quad \text{or} \quad \boxed{b = \frac{c}{2}}$$

4.3
The difference between $k$ and 9 is 4.

$$\boxed{k - 9 = 4}$$