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 \( =3 S-15 \) \( P-5=3 S-5 \) \( P \cdot 5=3 S \)

To solve for Sam's age, we need an equation that accurately reflects the information given about their ages from five years ago. The correct equation to complete the system is \( P - 5 = 3(S - 5) \). This represents the condition that five years ago, Pete’s age was three times Sam’s age. We can simplify this equation to find the exact ages. Now, if you want to solve it, we can replace \( P \) with \( 30 - S \) from the first equation. This gives us \( 30 - S - 5 = 3(S - 5) \), which simplifies to \( 25 - S = 3S - 15 \). Solving for \( S \), we find that Sam is 5 years old!