The question:

How many integral solutions does the equation 2x+3y=8 have such that 100<x<200?

Solution:

Blockquote

× = 4-3/2y (after rearranging)

Hence,

If x = 4, y = 0

If × = 7, y = - 2

If x= 10, y = -4

As given above, for integral solutions, the value of x increases in steps of 3, with the first integral value above 100 being 103. Hence, there are 33 integral solutions for the given range of x.

Wondering if anyone has a simpler approach? This would never be where my mind initial goes.