The salary scale in three school districts are as follows, for a teacher with a master’s degree:
District P: $30,000 plus $1500 for each year of experience
District Q: $30,000 plus $1750 for each year of experience
District R: $28,000 plus $1750 for each year of experience
a.Give a formula for the salary in each district for a teacher with n years of experience.
- P= 30,000 + 1500n
- Q= 30,000 + 1750n
- R= 28,000 + 1750n
b.Use your formulas to indicate the number of years experience teachers in Districts P and R when they earn the same salary.
- District P for 1 year= District R for 2 years.
c.Use your formulas to indicate the number of years experience teachers in Districts P and Q when they earn the same salary.
- District P for 7 years = District Q for 6 years.
d.Use your formulas to indicate the number of years experience teachers in Districts Q and R when they earn the same salary.
?? I've gone all the way to 36 and still haven't found it, and I wasn't sure if there was an easier way to do it.
there is no solution
they have the same experience step value; but the starting salaries are different
a Q teacher with equivalent experience will always have a $2000 higher salary than an R teacher
To find the number of years of experience when teachers in Districts Q and R earn the same salary, we can set their salary formulas equal to each other and solve for 'n', representing the number of years of experience.
The formula for District Q is Q = 30,000 + 1750n.
The formula for District R is R = 28,000 + 1750n.
Setting Q equal to R gives us:
30,000 + 1750n = 28,000 + 1750n
In this case, we notice that the '1750n' terms cancel each other out on both sides of the equation. We are left with:
30,000 = 28,000
This equation is not true since $30,000 is not equal to $28,000. Therefore, there is no number of years of experience when teachers in Districts Q and R earn the same salary.