Question

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

Answer 1

number=32+30=62

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Answer 2

Your answer should be 2,654

Answer 3

32x + 30 = 58y + 44 
we need to solve this for x and y, but they must both be integers. 

32x - 58y = 14 

32x = 14 + 58y 
x = (14 + 58y) / 32 
x = (7 + 29y) / 16 

so 7 + 29y must be divisible by 16. 
Trying various values of y, I found (7+29y) / 16 to equal 24 for y = 13. 
This means x = 24 and y = 13. 
so our number is 32x + 30 or 798. 

Hope this helps.

Answer 4

Take the number they're dividing by and multiply it out x1, x2, x3, etc. while adding the remainder.  Example (32x1)+30, (32x2)+30 do the same for the other number (58x1)+44 keep multiplying these out until you find a match. 

Here is an extrapolated example.  There can be multiple answers however 798 is the first one that comes up.