Question 1170839
let a be one of the integers.
let b be 33 more than 24 time the other.


your 2 equations are:


a * b = 9291.


a = 24 * b + 33


replace a with 24 * b + 33 in the first equation to get:


(24 * b + 33) * b = 9291


simplify to get:


24 * b^2 + 33 * b = 9291


subtract 9291 from both sides of the equation to get:


24 * b^2 + 33 * b - 9291 = 0


factor this quadratic equation to get:


b = -20.375 or 19.


b has to be an integer and has to be positive, so the answer is most likely b = 19.


replace b in the equation of a * b = 9291 to get:


a * 19 = 9291.


solve for a to get:


a = 9291/19 = 489.


replace a with 489 and b with 19 in the equation of a = 24 * b + 33 to get:
a = 24 * 19 + 33 = 489


both equations are satisfied when a = 489 and b = 19.


your solution is that the two integers are 489 and 19.