Question 1170801
new job = 900 a month plus 4.5% of the sales.
old job = 1200 a month plus 3.25% of the sales.


equation for new job is y = .045 * x + 900
equation for old job is y = .0325 * x + 1200


you want to know when the new job gives him better total compensation than the old job.


this occurs when .045 * x + 900 > .0325 * x + 1200


subtract 900 from both sides of the inequality and subtract .0325 * x from both sides of the inequality and simplify to get:


.0125 * x = 300


solve for x to get:


x = 300 / .0125 = 24,000


the new job will provide better compensation than the old job when sales exceed 24,000.


to confirm, select sales lower than 24,000, higher than 24,000, and equal to 24,000.


i picked 20,000, 30,000 and 24,000


at 20,000 sales, new job pays 900 + .045 * 20,000 = 1800 and old job pays 1200 + .0325 * 20,000 = 1850.
old job pays better.


at 30,000 sales, new job pays 900 + .045 * 30,000 = 2250 and old job pays 1200 + .0325 * 30,000 = 2175.
new job pays better.


at 24,000 sales, new job pays 900 + .045 * 24,000 = 1980 and old job pays 1200 + .0325 * 24,000 = 1980.
they pay the same.


you can graph these equations.
the graph will show you where the break even point is and when the new job starts paying more than the old job.


the graph is shown below.


<img src = "http://theo.x10hosting.com/2020/120101.jpg" >


red is the new job, blue is the old job.