Question

the sum of the first odd numbers in a set of three consecutive odd numbers is nine more than the third number. Find the greatest odd number

Answer 1

Simple.  Let the numbers be :  N,  N+2,  N+4    as consecutive odd numbers differ by 2. If N is odd, N+1 even, and N+2 will be odd. N+3 even and N+4 odd.

Sum of first two odd numbers =  N +    N + 2    =    9 +  N + 4
 so N = 11  Then greatest odd number N+4 is 15

Answer 2

let the no. be x
then first no.=x  ;second=x+2  and  third=x+4
:x+x+2=9+x+4     (according to question)
:2x-x=13-2
:x=11

first no=x=11;second=x+2=13 and third=x+4=15

check :11+13=15+9
              24=24
               LHS=RHS