Its likely because they are not enclosed correctly
$query = mysqli_query($mysqli, "SELECT * FROM table_name
WHERE Page LIKE ".$page."
AND Profession LIKE ".$profession."
AND Age LIKE ".$age."");
when compiled is something like
SELECT * FROM table_name
WHERE Page LIKE page number 1
AND Profession LIKE my profession
AND Age LIKE 100
which is invalid SQL
You need to use quotes and escape the values
$query = mysqli_query($mysqli, "SELECT * FROM table_name
WHERE Page LIKE '%".$page."%'
AND Profession LIKE '%".$profession."%'
AND Age LIKE '%".$age."%'");
would give
SELECT * FROM table_name
WHERE Page LIKE '%page number 1%'
AND Profession LIKE '%my profession%'
AND Age LIKE '%100%'
Which will likely give a result of what you would expect
Make sure the values are safe though by at bare minimum using http://www.php.net/manual/en/mysqli.real-escape-string.php though looking at prepared statements would be a better option
Edit:
Remove comma after LIKE ". $profession."