One number is three times another number. The difference between their product and their sum is 40.
Using this information, answer the following:
(i) Let the smaller number be x. Express the larger number in terms of x and set up an equation based on the given condition.
(ii) Reduce the relation of part (i) to a quadratic equation and solve it completely.
(iii) Hence, write the two numbers and verify that they satisfy the condition given in the question.