Sam Lloyd puzzle?

Question

The ages of Ann and Ben total 56 years.
Ben is twice as old as Ann was when
Ben was half as old as Ann will be when
Ann was 3 times as old as ben was when
Ben was 3 times as hold as Ann.

How old are they?

Answer 1

Step 1: Suppose Ann is A year old, and Ben is B year old now.
We will analyze the problem "backward".
Step 2: Start with the last phrase "When Ben was 3 times as old as Ann". If Ann was x-year-old, then Ben would be 3x at that time.
Step 3: Consider the phrase before the last. "when Ann is three times as old as Ben was". This means Ann will be 3(3x) = 9x year old.
Therefore, Benn will be 3x + (9x - x) = 11x year old at that time. (In deed, Ben's age here doesn't matter.)
Step 4: "when Ben was half as old as Ann will be". This means Ben was 9x/2 year old. Therefore, Ann was (9x/2 - 3x) + x = 5x/2 year old at that time.
Step 5: "Ben is twice as old as Ann was". This means Ben is 2(5x/2) = 5x year old now.
The chart below illustrates the problem:
Step 1, Step 2, Step 3, Step 4, Step 5
Name: Age now, Age was, Will be, Was, Now
Ann: A, x, 9x, 5x/2,
Ben: B, 3x, (11x), 9x/2, 5x
Three equations are obtained from the chart.
Ben's current age: B = 5x
Total of Ann and Ben's current ages: A + B = 56
(Difference of Ann's ages between Step 1 & 2) = (difference of Ben's ages between Step 1 & 2), that is
A - x = B - 3x
Solve the system of the simultaneous equations for A, B, and x.
B = 5x
A + B = 56
A - x = B - 3x
We have
x = 7
A = 3x = 21 (Ann)
B = 5x = 35 (Ben)

Answer 2

I suppose the other person (who has only negative points I notice - how d'ja do that?) was correct. My answer refers to your name - why the extra /n/ in the word greeneggsandNham?? Typo??