Find the greatest value with similar names

Question

Hello I am trying to figure out how to transform this table

+----+------------+-------+-------+---------------------+
| id | profile_id | name  | value |        added        |
+----+------------+-------+-------+---------------------+
|  1 |          1 | Item1 |   100 | 2018-11-30 17:08:38 |
|  2 |          1 | Item1 |   140 | 2018-11-30 17:18:38 |
|  3 |          1 | Item2 |   120 | 2018-11-28 17:08:38 |
|  4 |          2 | Item1 |   110 | 2018-11-03 17:08:38 |
|  5 |          3 | Item3 |   120 | 2018-11-30 17:08:38 |
|  6 |          3 | Item4 |   100 | 2018-11-29 17:08:38 |
+----+------------+-------+-------+---------------------+

Into something like this

+----+------------+-------+-------+---------------------+
| id | profile_id | name  | value |        added        |
+----+------------+-------+-------+---------------------+
|  2 |          1 | Item1 |   140 | 2018-11-30 17:18:38 |
|  3 |          1 | Item2 |   120 | 2018-11-28 17:08:38 |
|  5 |          3 | Item3 |   120 | 2018-11-30 17:08:38 |
|  6 |          3 | Item4 |   100 | 2018-11-29 17:08:38 |
+----+------------+-------+-------+---------------------+

Basically, it should display Unique 'name' and 'profile_id' (display maximum value of the 'value' field for a given name). I tried something like this

SELECT DISTINCT(t.profile_id),t.name,t.value FROM table as t ORDER BY t.value DESC;

There should be also a where clause that the added date cannot be older than 7d ays.

Further explanation: a profile_id can have the same names stored, only the value and added time will change. It should return only a unique name and the highest found value.

If I am not clear feel free to ask for more details.

Help is appreciated.