Part A
Her steps were

Kelsey made a mistake on line 3. Note how the 17/6 flips to 6/17. This is not correct. You keep the first fraction the same, but you do flip the second fraction. This only applies when you divide two fractions.
The third step should look like 
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Part B
Here's what she should have written

If you want to convert that improper fraction to a mixed number, then you could do something like this

Or you could divide 17 over 8 using long division to get 2 remainder 1. The 2 is the quotient that goes to the left of the 1/8. The remainder of 1 is the numerator of 1/8.
My answer is 38 students
( 22 students take one or both subjects)
3x + 9 + 3x =15
6x + 9 = 15
- 9 = -9
6x = 6
/6 /6
X =1
It is the right answer........
Alternate Interior Angles are a pair of angles on the inner side of each of those two lines but on opposite sides of the transversal.
1st question
angles 6 and 7
or
angles 2 and 3
2nd question
Angles 3 and 2
or
Angles 5 and 7