Set up and solve an equation for the following business situation.

Pitt's Pit Stop sold $$15,700\mathrm{.}50$ worth of gasoline yesterday. Regular sold for $$3\mathrm{.}30$ a gallon and premium sold for $$3\mathrm{.}45$ a gallon. If the station sold $360$ more gallons of regular than premium, answer the following questions.

$($a$)$ How many gallons of each type of gasoline were sold?

regular $$ gal premium $$ gal

$($b$)$ If the profit on regular gas is $$0\mathrm{.}15$ per gallon and on premium is $$0\mathrm{.}18$ per gallon, what was the station's total profit $($in dollars$)?$