The average of p, q, and 15 = $\frac{{p+q+15}}{3}$
The average of p, q, 15, and 35 = $\frac{{p+q+15+35}}{4}$

Since the averages are equal, $\frac{{p+q+15}}{3} = \frac{{p+q+15+35}}{4}$

Cross-multiply to get:
$4(p+q+15) = 3(p+q+15+35)$
$4p+4q+60 = 3p+3q+150$
$p+q = 90$

The average of p+q = $\frac{90}{2} = 45$

Also, here's a time saving property: If the average of a set of numbers remains the same after adding a single element of x, the average is equal to x. In this case, the average of {p, q, 15} remained the same after adding 35. Therefore, the average of {p, q, and 15} is 35.