We want to find three consecutive odd numbers.
Let the first odd number be x.
Then, the second one will be x + 2
The third will be x + 2 + 2, that is, x + 4
3 times the last number increased by the second is 50. That is:
[tex]3(x\text{ + 4) + (x + 2) = 50}[/tex]Solve that by expanding the bracket and collecting like terms:
[tex]\begin{gathered} 3x\text{ + 12 + x + 2 = 50} \\ 3x\text{ + x + 12 + 2 = 50} \\ 4x\text{ + 14 = 50} \\ 4x\text{ = 50 - }14 \\ 4x\text{ = 36} \\ x\text{ = 36/4} \\ x\text{ = 9} \end{gathered}[/tex]Therefore, the three consecutive numbers are:
x = 9
x + 2 = 11
x + 4 = 13
9, 11 and 13
