The first sentence is:
My brother is 7 years younger than ('my age'). It mentions 'my age' second, so:
Let this bar be 'my age':

And since the brother BRO is 7 years younger, we use a shorter bar for 'BRO's age'.
  
Now notice that "my age" can be partitioned off into 'bro's age' and 7 more,
like this:

Now we look at the next sentence:
Twice my age plus 3 times his age is 99.
So we make 2 long bars for 'my age' and 3 short bars for 'bro's age':


Now let's partition off the bars for 'my age' as we did above:



Now we count the BRO's and there are 5 of them.
We count the 7's and there are 2 of them, so the equation is

                      5 BRO's + 2 7's = 99
or                           5B + 2x7 = 99
                              5B + 14 = 99
 Subtract 14 from both sides:      5B = 85
 Divide both sides by 5:            B = 17

BRO is 7 years younger, so 'your age' is 17 + 7 or 24.

Edwin

Mentally, reduce your age by 7 years, to the age of your brother.

Then "twice my age plus 3 times his age" will become 99 - 2*7 = 85.


Now this "twice my age plus 3 times his age" is the same as 5 times the brother age.


Hence, the brother age is 85/5 = 17 years, and your real age is 7 years more, or 17+7 = 24 years.


ANSWER.  You are  24 years old. Your brother is 17 years old.