algebra help please...?

Question

can 1000 as the sum of two positive integers, one of which is divisible by 11 and the other by 17?

Answer 1

Of course.
Just subtract 17 from 1000 and see if the result is divisible by 11. If so you have a solution: one 17, and however many 11's you get when you divide.

If that doesn't work, subtract 2 17's from 1000 and see whether the remainder is divisible by 11. If so, the answer is two 17's, and some number of 11's.

Keep trying by subtracting another 17 from 1000 and dividing by 11.

At most, you'll have to do this 10 times to get an answer.

And once you've found an answer, you can find another answer by subtracting 17's. But now don't subtract ONE 17; subtract another ELEVEN 17's to find the next number that will be divisible by 11. (i.e., subtract 11 x 17 = 187)

There should be about 6 ways to express 1000 as the sum of multiplies of 11 and 17.

Answer 2

9*17 = 153
77*11 = 847

847 + 153 = 1000