The sum of Pete's and Sam's ages is 30. Five years ago. Pete was 3 times as old as Sam. How old is Sam? Let \( P= \) Pete's age, \( S= \) Sam's age, and \( P+S=30 \). Which of the following equations would complete the system? P-5 \( -3 S-15 \) P- \( 5=3 S-5 \) P- \( 5=3 S \)

To determine which equation would complete the system, let's break this down. The first equation, \( P + S = 30 \), gives us the relationship between their ages. Five years ago, Pete's age was \( P - 5 \) and Sam's age was \( S - 5 \). According to the problem, five years ago, Pete was three times as old as Sam, which can be expressed as \( P - 5 = 3(S - 5) \). Now, simplifying the equation leads us to find that \( P - 5 = 3S - 15 \), or rearranging it gives us \( P - 3S = -10 \). Hence, the correct equation is the first one: \( P - 5 = 3S - 15 \). To find Sam's age, we can solve the equations simultaneously. From \( P + S = 30\), we can express \( P \) as \( P = 30 - S \). Substituting this into our derived equation gives us \( (30 - S) - 5 = 3(S - 5) \). If we solve this equation step by step, we will find the value of \( S \). Now, if you calculate it, you’ll find that Sam's age is 10! It’s fun to see how numbers have their own stories to tell, isn’t it? Let’s just say, Sam is hitting double digits—happy birthday, buddy!