"These wordy puzzles are confusing enough to make me want to pull my hair out (I'm nearly in need of a wig myself after that one).
If the age of the wig now is \( W \), the age of the judge now is \( 56 - W \).
Therefore, the age of the judge back then is \( W \) and the age of the wig back then is \( \frac{56 - W}{2} \).
The age difference of the wig then and now must match the age difference of the judge then and now.
So \( W - \frac{56 - W}{2} = (56 - W) - W \)
Simplify a wee bit by multiplying out brackets:
\( W - 28 + \frac{W}{2} = 56 - 2W \)
Double the whole thing to get rid of that pesky half:
\( 2W - 56 + W = 112 - 4W \)
Rearrange to get:
\( 7W = 168 \)
So \( W = 24 \).
The wig is 24 now and the judge is 32.
The rest of the clues, which describe the situation eight years ago, are easily verified from here!
"
Kevin, Australia
Saturday, June 1, 2024
"This is my solution but I am not entirely confident 🙂
Now Judge age is \( x \) Wigs age is \( y \)
Then Judge age is \( y \) Wigs age is \( y \) – difference in judges ages = \( y – (x – y) = 2y – x \)
Sunil, New Zealand
Saturday, June 1, 2024
"
"
Chris Smith, Scotland
Saturday, June 1, 2024
"These wordy puzzles are confusing enough to make me want to pull my hair out (I'm nearly in need of a wig myself after that one).
If the age of the wig now is \( W \), the age of the judge now is \( 56 - W \).
Therefore, the age of the judge back then is \( W \) and the age of the wig back then is \( \frac{56 - W}{2} \).
The age difference of the wig then and now must match the age difference of the judge then and now.
So \( W - \frac{56 - W}{2} = (56 - W) - W \)
Simplify a wee bit by multiplying out brackets:
\( W - 28 + \frac{W}{2} = 56 - 2W \)
Double the whole thing to get rid of that pesky half:
\( 2W - 56 + W = 112 - 4W \)
Rearrange to get:
\( 7W = 168 \)
So \( W = 24 \).
The wig is 24 now and the judge is 32.
The rest of the clues, which describe the situation eight years ago, are easily verified from here! "
Kevin, Australia
Saturday, June 1, 2024
"This is my solution but I am not entirely confident 🙂
Now Judge age is \( x \) Wigs age is \( y \)
Then Judge age is \( y \) Wigs age is \( y \) – difference in judges ages = \( y – (x – y) = 2y – x \)
So \( x = 2(2y – x) \)
Hence \( x = 4y – 2x \)
So \( 3x = 4y \)
\( x = \frac{4y}{3} \)
Sum of ages now \( x + y = 56 \)
So \( \frac{7y}{3} = 56 \)
\( y = 24 \) Wig age now
\( x = 32 \) Judge age now "