When a number is divided by 13 the remainder is 11 . when the same number is divided by 17 remainder is 9. what is the number

 → 13p + 11 − 13p − 11 = 17q − 13p + 9 − 11 ; 

to get: 

→ 0 = 17q − 13p − 2 ; ↔ 17q − 13p − 2 = 0 ; 

→ Add "2" to each side of the equation; 

  → 17q − 13p − 2 + 2 = 0 + 2 ;

  → to get:  17q − 13p = 2 ; 

Now, solve for "q", by isolating "q" on one side of the equation:

→ We have: 17q − 13p = 2 ; 

→ Add "13p" to EACH side of the equation:  17q − 13p + 13p = 2 + 13p ;

→ to get: 17q = 2 + 13p ;

→Now, divide EACH side of the equation by "17"; to isolate "q" on one side of the question, and to solve for "q" ;

→  17q / 17 = (2 + 13p) / 17 ;

 → q = (2 + 13p) /17

→ x = (338)  + 11 ; 

→ x  = 349;  which is our answer.

Let us check our answer.

Given: 

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