Adding the equations to eliminate p would be the correct step because when you add the equations together, the variable p would cancel out and be eliminated leaving you with 2w=35 you can then solve for the value of w which you can then input to find the value of p, allowing you to solve for the values of both p and w.
Inequality, because want to know when we'll make a profit.

Profit: Let's See When 280d equals 52000

So, after 190 days Julianne will make a profit
I'm not good at graphing, but desmos.com is an online graphing calculator that works really well.
This is not an integer; an integer is a whole number that can be positive, negative, or zero such as -1, 0, and 1.