Gabriel earns \( \$ 11.25 \) per hour at his job. He also receives a bonus of \( \$ 20 \) each week if he arrives on time for each of his shifts. Assume that Gabriel is always on time, and \( x \) is the number of hours he works. Which rule for \( f(x) \) models his weekly paycheck? \( f(x)=31.25 x \) \( f(x)=20 x+11.25 \) \( f(x)=11.25 x \) \( f(x)=11.25 x+20 \)

To model Gabriel's weekly paycheck, we need to consider both his hourly wage and his weekly bonus. He earns \( \$11.25 \) for every hour worked, which can be represented as \( 11.25x \). Additionally, since he receives a bonus of \( \$20 \) for being on time, we need to add that to his earnings. Thus, the correct rule for \( f(x) \) that models his weekly paycheck is \( f(x) = 11.25x + 20 \). So, the answer is \( f(x) = 11.25x + 20 \). Now that we’ve clarified that, here’s some more interesting information! If you’re curious about how paycheck calculations have evolved, consider the history of labor regulations. In the past, workers often faced harsh conditions and inconsistent pay, so systems like hourly wages and bonuses were essential in creating fairer work environments. These regulations evolved further with labor unions advocating for fair pay and on-time bonuses like Gabriel's! For a real-world application, trying to budget your salary is invaluable. If you want to plan future expenses, remember to factor in any bonuses you regularly receive, like Gabriel's. Knowing how to calculate your total earnings weekly can help you save for vacations, large purchases, or even just ensure you have enough funds until the next paycheck!