Question 322933
Assign variables to your integers.
The first (or smaller) will be X
Because they are consecutive ODD integers you will add 2 to the first integer to find the second.
So the second (larger) will be X+2

"twice the larger is 17 more than the smaller" translates to

2(x+2)=x+17

now solve for x

2x+4-4=x+17-4
2x-x=x+13-x
x=13  so 13 is your first, smaller integer. 
x+2=15 so 15 is your second, larger integer.

*check*
twice the larger is 17 more than the smaller

2(15)=(13)+17
30=30