SOLUTION: donovan is a salesperson at a car dealership. last month he sold 11 cars and earned 6300 in base salary and commissions. this month he sold 24 cars and earned 12800 in base salary

Algebra ->  Linear-equations -> SOLUTION: donovan is a salesperson at a car dealership. last month he sold 11 cars and earned 6300 in base salary and commissions. this month he sold 24 cars and earned 12800 in base salary      Log On


   



Question 514288: donovan is a salesperson at a car dealership. last month he sold 11 cars and earned 6300 in base salary and commissions. this month he sold 24 cars and earned 12800 in base salary and commissions. finda a linear equation that describes the amount donovan earns in commissions (y) for selling x cars.
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
You want to end up with an equation
that looks like +y+=+m%2Ax++
+x+ = cars sold per month
+y+ = commission
+b+ = base salary
There is no constant on the right side because
commission only depends on number of cars sold
-------------------
Using given data, I can say:
(1) +y%5B1%5D+=+6300+-+b+
(2) +y%5B2%5D+=+12800+-+b+
Subtract (1) from (2)
(2) +y%5B2%5D+=+12800+-+b+
(1) +-y%5B1%5D+=+-6300+%2B+b+
+y%5B2%5D+-+y%5B1%5D+=+6500+
I can say
+%28+y%5B2%5D+-+y%5B1%5D+%29+%2F+%28+x%5B2%5D+-+x%5B1%5D+%29+=+m+
+6500+%2F+%28+24+-+11+%29+=+m+
+m+=+6500+%2F+13+
+m+=+500+
The equation is
+y+=+500x+
Here's the plot ( in hundreds of dollars )
+graph%28+400%2C+400%2C+-2%2C+12%2C+-1%2C+20%2C+5x+%29+
I can also find base salary
+y%5B1%5D+=+500x%5B1%5D+
+y%5B1%5D+=+500%2A11+
+y%5B1%5D+=+5500+
and
+y%5B2%5D+=+500x%5B2%5D+
+y%5B2%5D+=+500%2A24+
+y%5B2%5D+=+12000+
and
+6300+=+5500+%2B+b+
+b+=+800+
also
+12800+=+12000+%2B+b+
+b+=+800+
base salary is $800