Answer:
29
Step-by-step explanation:
Let the smaller integer be x.
The other integer is 1 greater than 3 times x, or 3x + 1.
The product is 154.
x(3x + 1) = 154
3x^2 + x - 154 = 0
157 = 2 * 7 * 11
14 * 11 = 154
22 * 7 = 154
(3x + 22)(x - 7) = 0
3x + 22 = 0 or x - 7 = 0
3x = -22 or x = 7
x = -22/3 or x = 7
-22/3 is not a positive integer, so we discard that solution.
The smaller integer is 7.
3x + 1 = 3(7) + 1 = 22
The greater integer is 22.
The sum of the integers is 7 + 22 = 29
