I need help with Algebra 1

Question

Donna signed a job contract that states that she will be paid an hourly rate of $9.95 for her first year of work and will receive a raise of $0.85/h every year after that.

In what year will Donna’s hourly rate be $34.60?

a year 28

b year 29

c year 30

d year 31

Answer 1

You need to write an expression for her hourly rate in terms of the number of years.

 

She starts with a rate of 9.95 in year 1.  Add 0.85 to that in year 2.  And again in year 3, and so on.

 

So the amount that's added on top of her starting rate is 0.85 time the number of years MINUS 1.  The minus 1 is because she only starts getting raises in the SECOND year.

 

So the expression for her hourly rate would be 9.95 + 0.85 y, where y is the number of years.

 

So to answer the problem, set that expression to 34.60 and solve:

 

9.95 + 0.85 (y - 1) = 34.60

 

Simplify:

9.95 - 0.85 y - 0.85 = 34.60

9.1 - 0.85 y = 34.60

 

Subtract 9.1 from both sides:

0.85 y = 34.60 - 9.1 = 25.5

 

Divide both sides by 0.85

y = 25.5 / 0.85

 

y = 30

 

So the answer is c, year 30

 

 

Answer 2

$9.95+$0.85h=$34.60

0.85h=34.60-9.95

0.85h=24.65

85h=2465

h=2465/85

h=29 years, answer c

As Jon wrote, it takes 29 years after her first year to make that rate.

So the answer, as Jon said, is year 30, c.