Gabe paid $ 120 for 3 shirts and 2 pairs of pants. Each shirt cost $15.
Each pair of pants cost the same amount.
The equation 3s + 2p = 120 can be used to determine p, the cost of each pair of pants.

Gabe solved the equation using the following steps:

3s + 30=120

3s= 90

s= 30

Therefore, Gabe calculates the cost for each pair of pants as $30. Did Gabe find the cost for each pair of pants correctly?

If he did, justify each step of Gabe's solution using mathematical properties.
If he did not, describe any error Gabe made in his calculations and determine the price of each pair of pants.