13 Siti had 135 buttons. $$ \frac{5}{9} $$ of the buttons were red and the rest were blue. She used 64 red buttons and bought some more blue buttons. She had 84 buttons left in the end. How many blue buttons did Siti buy?

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1. Calculate the number of red and blue buttons Siti initially had:
   - Red buttons:  
     $$
     \frac{5}{9} \times 135 = 75
     $$
   - Blue buttons:  
     $$
     135 - 75 = 60
     $$

2. Determine the remaining red buttons after using 64 red buttons:
   $$
   75 - 64 = 11
   $$

3. Let $$ x $$ be the number of blue buttons Siti bought. After her actions, the total number of buttons is the sum of the remaining red buttons and all blue buttons (initial plus bought):
   $$
   11 + (60 + x) = 84
   $$

4. Solve the equation:
   $$
   11 + 60 + x = 84
   $$
   $$
   71 + x = 84
   $$
   $$
   x = 84 - 71 = 13
   $$

Siti bought $$ 13 $$ blue buttons.
Siti bought 13 blue buttons.

13 Siti had 135 buttons.
of the buttons were red and the rest were blue.
She used 64 red buttons and bought some more blue buttons.
She had 84 buttons left in the end.
How many blue buttons did Siti buy?

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13 Siti had 135 buttons. of the buttons were red and the rest were blue. She used 64 red buttons and bought some more blue buttons. She had 84 buttons left in the end. How many blue buttons did Siti buy?