Solution

2x+3y=515.

By making x as subject, we have,

x = $\frac { 515-3y }{ 2 }$ .

So, the numerator should be divisible by 2 and y and x are positive integers.

Moreover, y can take only odd values because numerator should be of the form 2n. (odd-odd = even) and (odd-even=odd).

So, y can take values 1,3,5,7,............................. till x remains positive.

$\left[ \frac { 515 }{ 3 } \right]$ is 171 which is the limiting value of y.

So, number of values that y can take is equal to total solutions = 172/2 = 86.

Here, $\left[ x \right]$ means box function or greatest integer function.

The no of positive solution in integer of ax + by = n is give by n/[a,b] + 1

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