The problem is almost solved correctly, but let’s clarify the approach to verify each step and correct any inaccuracies.

Problem Statement Recap:

• Let $B$ and $S$ represent the current ages of the brother and sister, respectively.
• Total age of the brother and sister is 46 years: $B + S = 46$.
• Seven years ago, the sum of their ages was four times the brother’s age.

Solution Steps:

1. Express the situation from seven years ago:

   • Seven years ago, the brother’s age was $B - 7$, and the sister’s age was $S - 7$.
   • According to the problem, seven years ago, the sum of their ages was four times the brother’s age: $(B - 7) + (S - 7) = 4(B - 7)$

2. Simplify the equation from seven years ago: $B + S - 14 = 4B - 28$ Rearranging terms gives: $S = 3B - 14$

3. Use the current age relationship: