Final answer:
The consecutive odd integers are 1,789 and 1,791.
Step-by-step explanation:
Let's represent the two consecutive odd integers as x and x + 2. The sum of these two numbers is given as 3,580, so we can write the equation:
x + (x + 2) = 3,580
Combine like terms:
2x + 2 = 3,580
Subtract 2 from both sides of the equation:
2x = 3,578
Divide both sides of the equation by 2:
x = 1,789
Therefore, the first odd integer is 1,789, and the second odd integer is 1,789 + 2 = 1,791.