Ken left a job paying $ 75,000 per year to accept a sales job paying $ 45,000 per year plus 15 percent commission. If each of his sales is for $ 750, what is the least number of sales he must make per year if he is not to lose money because of the change?

Question: Ken left a job paying $ 75,000 per year to accept a sales job paying $ 45,000 per year plus 15 percent commission. If each of his sales is for $ 750, what is the least number of sales he must make per year if he is not to lose money because of the change?

Solution:
In order not to lose money because of the change Ken's total commission must be at least $ 75,000 - $ 45,000 = $ 30,000,
so total sales must be at least $ 30,000/0.15 = $200,000.

Which means that he must make at least $ 200,000/750 = 800/3 = 266.6 sales ≈ 267 sales.