When the smaller of two consecutive integers is added to four times the larger the result is 49?

Let the smaller integer be ( n ) and the larger integer be ( n + 1 ). The equation based on the problem statement is ( n + 4(n + 1) = 49 ). Simplifying this gives ( n + 4n + 4 = 49 ), or ( 5n + 4 = 49 ). Solving for ( n ) gives ( 5n = 45 ), so ( n = 9 ). Thus, the two consecutive integers are 9 and 10.