pete gets paid $35 per hour to fix the blinking lights at the top of radio transmission towers, and this week, since there are no thunderstorms in the forecast, he plans to work five hours overtime. By week's end, the government will have taken $462 in taxes out of his check, leaving him a total of $1,463. How many hours does pete normally work per week?
Let's denote Pete's normal working hours per week as x.
His overtime hours will be 5.
His total working hours will be x + 5.
His total income before taxes will be 35 * (x + 5).
After taxes, his income will be 35 * (x + 5) - 462.
We are told that his total income after taxes is $1,463, so we can set up the equation as follows:
35 * (x + 5) - 462 = 1,463.
Expanding the equation, we get: 35x + 175 - 462 = 1,463.
Combining like terms, we have: 35x - 287 = 1,463.
Adding 287 to both sides of the equation results in: 35x = 1,750.
Finally, dividing both sides of the equation by 35 gives us: x = 50.
Therefore, Pete normally works 50 hours per week. Answer: \boxed{50}.