If you're struggling to set up your inequalities, just group things together. The $10 for babysitting and the $20 for sales are associated with the $50 minimum. So if we say there's "b" number of babysitting hours and "s" number of sales hours, then that means that the amount worked during a day is b+s. We know that that must be less than or equal to 5. Next, multiply each of those variables by the pay, and you get the total pay for the day equal to 10b+20s, which we know is at least 50. This gives us the inequalities:
b + s ≤ 5
10b + 20s ≥ 50
If you're looking for corner points of the graph, we could divide everything in the second inequality by 10 to get b + 2s ≥ 5. Note that the corner points can be identified graphically as (0, 2.5), (0, 5), and (5, 0) (simply put these inequalities into Desmos graphing calculator to view this). This means that the maximum income should be at one of these points. Plugging in the income for each, we find that if she works entirely at the sales job, she will earn $100 dollars per day.
