Sal sold 16 pairs of socks in total. Type 'a' socks cost R45 per pair and type 'b' socks cost R30 per pair. If Sal made R585 in total, how many pairs of type 'b' socks did she sell?

Let $a$ be the number of pairs of type 'a' socks sold.
Let $b$ be the number of pairs of type 'b' socks sold.

From the problem statement, Sal sold 16 pairs in total:

$$a + b = 16 \quad (1)$$

The price for type 'a' socks is R45 per pair, and for type 'b' socks is R30 per pair. The total income was R585:

$$45a + 30b = 585 \quad (2)$$

From Equation (1), we can express $a$ in terms of $b$:

$$a = 16 - b$$

Substitute $a = 16 - b$ into Equation (2):

$$45(16 - b) + 30b = 585$$

Distribute 45:

$$720 - 45b + 30b = 585$$

Combine like terms:

$$720 - 15b = 585$$

Subtract 720 from both sides:

$$-15b = 585 - 720$$ $$-15b = -135$$

Divide by -15:

$$b = \frac{-135}{-15}$$ $$b = 9$$

Sal sold 9 pairs of type 'b' socks.

The number of pairs of sock b Sal sold is $\text{9 pairs}$.