the two consecutive positive integers can be written as

x and x+1

where x is positive integer

the product of one integer and triple the other is 720

x*3*(x+1) = 720

by solving we find

x = 15

click here to see the step by step solution of the equation

15 + 1 = 16

15 + 16 = 31

the sum of these two integers is 31.