I am a number less than 3000. When you divide me by 32, my remainder is 30. When you divide me by 58, my remainder is 44. What number am I?

Question

Not understanding the process. 

Answer 1

Let Q1 and Q2 be the quotients from dividing 32 and 58 respectively.

Then 32 Q1 + 30 = 58 Q2 + 44

32 Q1 = 58 Q2 + 14

16 Q1 = 29 Q2 + 7

16 Q1 = (16 + 13)Q2 + 7

16 Q1 = 16 Q2 + 13 Q2 + 7

16(Q1 - Q2) = 13 Q2 + 7

Because Q1 and Q2 are integers, we have to find Q2 whereby 13Q2 + 7 is divisible by 16.

After some try-and-error, we get Q2 = 13.  That is 13*13 + 7 = 176

Therefore, Q1 - Q2 = 11  -->  Q1 - 13 = 11  -->  Q1 = 24

32*24 + 30 = 58*13 + 44 = 798.

I am 798