If the larger of two numbers were decreased by three hundred forty-nine, then the two numbers would be the same. The sum of the two numbers is 735. What are the numbers?

Let the first number be x

Therefore the other number is equal to (x + 349)

x + (x + 349) = 735

x + x + 349 = 735

2x = 386

x = 193

x + 349

=193 + 349

=542

Thus the two numbers are 193 and 542.