Question 906256
x is the first number
x+1 is the second number.


you get:


x + x + 1 = 35
x * (x+1) = 306


simplify to get:


2x+1 = 35
x^2+x = 306


from the first equation, solve for x to get x = 17.


it looks like one of your numbers has to be 17.


then the other number must be 18 because the numbers are consecutive starting from 17.


multiply 17 * 18 and you get 306 so this confirms that the numbers are 17 and 18.


if you had solved for x in the second eqaution, it would have given you x = 17 as well.


x^2 + x = 306 is the second equation.
subtract 306 from both sides of the equation to get x^2 + x - 306 = 0
factor the equation to get (x+18) * (x-17) = 306
solve for x to get x = -18 or x = 17


x can't be -18 because -18 * -17 results in -306 and not 306.
therefore x has to be 17.


17*18 = 306
17+18 = 35


since you are asked to find the smaller number, then your solution is that the smaller number is equal to 17.