SOLUTION: Solve the following problems by using elimination or substitution. Make sure to define your variables, write a system, solve showing all work and write a complete sentence answer.

Question 1170801: Solve the following problems by using elimination or substitution. Make sure to define your variables, write a system, solve showing all work and write a complete sentence answer.
Robert has a job offer in which he will receive $900 a month plus a commission of 4.5% of the total price of the cars that he sells. His current job pays him $1200 a month plus a commission of 3.25% of the total price of the cars that he sells. How many sales would he need each month to make the new job a better deal?

Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!
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.

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

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