Sal sold 16 pairs of socks for a total of 585. Type a socks cost 45 per pair and type b socks cost $30 per pair. How many pairs of sock b did Sal sell?

Let $a$ be the number of pairs of sock type $a$.
Let $b$ be the number of pairs of sock type $b$.

From the problem statement, we have two pieces of information:

1. Total number of pairs sold:

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

2. Total income from sales:

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

$$45 \times 16 - 45b + 30b = 585$$ $$720 - 45b + 30b = 585$$ $$720 - 15b = 585$$

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

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

Sal sold 9 pairs of sock type $b$.

$$a = 16 - b = 16 - 9 = 7$$

Check total income: $45(7) + 30(9) = 315 + 270 = 585$. This matches the given total income.

The number of pairs of sock $b$ Sal sold is:

$$9$$