SOLUTION: You are applying to be a salesperson for a local used car company. You have a choice to make that may greatly affect your income. You may choose a base salary of $25,000 per year

Algebra ->  Rational-functions -> SOLUTION: You are applying to be a salesperson for a local used car company. You have a choice to make that may greatly affect your income. You may choose a base salary of $25,000 per year      Log On


   



Question 763747: You are applying to be a salesperson for a local used car company. You have a choice to make that may greatly affect your income. You may choose a base salary of $25,000 per year plus a commission of 10% on sales that you make, or you may choose a base salary of $35,000 per year plus 7.5% commission on all sales you make.
a) Letting x = the number of dollars in sales that you may make, and y1 = and y2 = the first and second annual earnings options, respectively, write two equations (a system) as described by the options given above.
I can't come up with anything that makes sense!!! Please Help

Found 2 solutions by MathTherapy, KMST:
Answer by MathTherapy(10552) About Me  (Show Source):
You can put this solution on YOUR website!

You are applying to be a salesperson for a local used car company. You have a choice to make that may greatly affect your income. You may choose a base salary of $25,000 per year plus a commission of 10% on sales that you make, or you may choose a base salary of $35,000 per year plus 7.5% commission on all sales you make.
a) Letting x = the number of dollars in sales that you may make, and y1 = and y2 = the first and second annual earnings options, respectively, write two equations (a system) as described by the options given above.
I can't come up with anything that makes sense!!! Please Help

1st option: x = sales amount, and commission = 10% of sales, or 10% of x, or .1x
Total earnings if 1st option is chosen: y%5B1%5D+=+.1x+%2B+25000

2nd option: x = sales amount, and commission = 7.5% of sales, or 7.5% of x, or .075x
Total earnings if 2nd option is chosen: y%5B2%5D+=+.075x+%2B+35000

Answer by KMST(5328) About Me  (Show Source):
You can put this solution on YOUR website!
For the first option you would get $25,000 plus 0.10 (10%) times the amount of your sales, so
y%5B1%5D=25000%2B0.1x
For the second option you would get $35,000 plus 0.075 (7.5%) times the amount of your sales, so
y%5B2%5D=35000%2B0.075x


The amount of sales, and income at the point that would make both options equivalent is the solution to
system%28y=0.1x%2B25000%2Cy=0.075x%2B35000%29 --> 0.1x%2B25000=0.075x%2B35000 --> 0.1x-0.075x=35000-25000 --> 0.025x=10000 --> x=10000%2F0.025 --> highlight%28x=400000%29
y=0.1%2A400000%2B25000 --> y=40000%2B25000 --> highlight%28y=65000%29