The person was driving $100$ miles per hour.
Work Step by Step
For this problem, we know that the fine, denoted $F$, is $400$. We can now substitute $400$ for $F$ into the equation given to solve for $x$, the speed of the car in miles per hour. $$400 = 10(x - 65) + 50$$ First, we use distributive property to simplify the equation: $$4000 = 10x + 10(-65) + 50$$ Multiply: $$400 = 10x - 650 + 50$$ Group like terms: $$400 = 10x + (-650 + 50)$$ Do the addition: $$400 = 10x + (-600)$$ To add a negative number means to subtract that number: $$400 = 10x - 600$$ Add $600$ to both sides of the equation to isolate constants to one side of the equation: $$1000 = 10x$$ Divide both sides by $10$ to solve for $x$: $$x = 100$$ The person was driving $100$ miles per hour.