How many pppaaaaiirrsss???

Because x and y are positive integers one of the terms must be a multiple of 3. Since there are 33 multiples of 3 under 100 the answer is 33.

x + 3y = 100

x = 100 – 3y maximum value 100/3 = quotient 33

Rearranging gives us $x=100-3y$ . Since $x$ is by itself with $1$ as its coefficient, that means that all values of $y$ will make this equation true as long as $x>0$ (from the equation above). The possible values of $y$ are $1,2,3,......,32,33$ . So the number of the pairs of solutions is $\boxed{33}$

$x+3y=100$ $\Rightarrow$ $y=33+\frac { 1-x }{ 3 }$ $\Rightarrow$ $x=1,4,7,..............97$ This is because it is given that x and y is positive and also an integer hence the possible values are as given above. There are 33 values of x hence there are 33 pair of solutions (x,y) for $x+3y=100$ .