Hourly Rate Simplify

Question

You are paid $1.5​ times your normal hourly rate for each hour you work over $30​ hours in a week. You work $31​ hours this week and earn $561.96​ . What is your normal hourly rate?

Answer 1

Given:

Let h = Your hourly rate

Let 1.5h = Your hourly rate for any hours you work over 30.

Let x = Number of hours you worked at your overtime rate of pay.

Let y = Number of hours you worked at your normal rate of pay.

Let p = the amount of money you get paid.

Need:

h = ? Calculate your hourly rate.

In this problem, we know that x = 1 hour, and y = 30 hours

x + y = your total hours for the week = 30 + 1 = 31 hours.

The key to this problem is setting up an algebra equation that properly models this situation.

x = (Hours Worked) - 30 = 31 - 30 = 1 hour

We can now write an algebraic relation between our variables.

p = hy +1.5xh

In this equation, hy and 1.5xh are like terms because they have the same units.

h ($/hour), x(hours), y(hours), and 1.5 is a constant.

Since they are like terms, we can combine them.

p = (1.5x + y)h

we know what p is, and we know what x and y are.

We are solving for h, so lets get h by itself.

h = p / (1.5x + y)

$561.96 = $561.96 = $17.84 = h

--------------------------------- -------------- ----------

(1.5 * 1 hour) + 30 hours 31.5 hours hour

Answer 2

Hi Autumn M

You have $ attached to all your numbers so I have a question for you below.

Were you trying to say that you are paid 1.5 times your normal hourly rate for each hour you work over 30 hours in a week. You worked 31 hours this week and earned a total of $561.96?

According to this you worked

30 hours at your regular pay rate and 1 extra hour at 1.5 times your regular pay rate.

The information below may be useful in terms of pay

Let x = regular pay

Let 30x = pay for regular hours

Let 1.5x = pay for hours over 30

Total is $561.96

30x + 1.5x = 561.96

31.5x = 561.96

x = 561.96/31.5

x = 17.84

We can check by substituting this in the equation above

30(17.84) + 1.5(17.84) = 535.20 + 26.76 = 561.96

I hope this helps please let me know if interpreted your question incorrectly.