Six years ago, Anita was P times as old as Ben was. If Anita is now 17 years old, how old is Ben now in terms of P?

Introduction / Context: This age problem introduces a parameter P that represents how many times older Anita was than Ben six years ago. We are asked to express Ben s present age in algebraic form in terms of P, using the fixed current age of Anita.

Given Data / Assumptions:

• Present age of Anita = 17 years.
• Let present age of Ben = B years.
• Six years ago, Anita s age was P times Ben s age at that time.
• We must express B in terms of P.

Concept / Approach: Six years ago, Anita s age was 17 - 6 = 11 years, and Ben s age was B - 6 years. The condition that Anita was P times as old as Ben can be written as: 11 = P(B - 6). We then solve this linear equation for B in terms of P. No numerical value of P is given, so the answer must stay in symbolic form.

Step-by-Step Solution: Anita s present age = 17 years. Six years ago, Anita s age = 17 - 6 = 11 years. Let Ben s present age = B years. Six years ago, Ben s age = B - 6 years. Given: Anita s age six years ago was P times Ben s age then. So 11 = P(B - 6). Divide both sides by P: B - 6 = 11 / P. Therefore B = 11 / P + 6. So Ben s present age is 11/P + 6 years.

Verification / Alternative check: We can test with a simple hypothetical value of P. Suppose P = 1, meaning Anita and Ben were the same age six years ago. Then Ben s present age formula gives B = 11/1 + 6 = 17, the same as Anita s present age, which matches the interpretation that they had the same age six years ago and have both aged the same amount since then.

Why Other Options Are Wrong: Option P/11 + 6 incorrectly inverts the fraction. Option 17 - P/6 mixes units (years) with a variable divisor, which does not follow from the equation 11 = P(B - 6). Option 17/P ignores the six-year difference entirely and does not incorporate the fixed difference between present and past ages.

Common Pitfalls: A common mistake is to write P = 11(B - 6) or to misread P times as 11/P. Another error is forgetting to subtract 6 from both ages when going back in time. Always carefully reconstruct the situation at the earlier time before writing your equation.

Final Answer: Ben s present age, in terms of P, is 11/P + 6 years.