Let's call the our odd numbers [tex]a[/tex], [tex]b[/tex], and [tex]c[/tex], in ascending order. It can be said then that [tex]b = a +2[/tex] (It is the next odd number after [tex]a[/tex]) and [tex]c = a + 4[/tex] (It is the second consecutive number after [tex]a[/tex]).
Additionally, we can say:
[tex]c + 2a = 25[/tex]
Now, how about we substiute in the value for [tex]c[/tex] we found in the first paragraph for [tex]c[/tex] in the preceeding equation? This gives us:
[tex](a + 4) + 2a = 25[/tex]
[tex]3a + 4 = 25[/tex]
[tex]3a = 21[/tex]
- Subtract 4 from both sides
[tex]a = 7[/tex]
We have found that the smallest number is 7. Substituting this into the equations we found in the first paragraph, we find:
[tex]b = 7 +2 = 9[/tex]
[tex]c = 7 + 4 = 11[/tex]
The numbers are 7, 9, and 11.
