"A woman earns 10.00 per hour at her job, but if she works more than 20 hours in a week she is paid 1.5 times her regular salary for the overtime hours worked. One week her gross pay was 275. How many overtime hours did she work that week?

Express your answer in hours to 2 significant figures."

I'm not sure how to start the problem. I tried something like:

10(h) + ??? = 275 hours but that doesn't seem like the right equation.

let the number of overtime hours be x

275 = 10(20) + 15x
solve for x

I got x = 5

check
20 hours at $10 = 200
5 hours at $15 = 75
total = 275 , yeahhh

what is 1.5 of $10 ?

20 hours at $10 = 20(10) = 200
x hours at $15 = x(15) = 15x

Where did you get the 15x from?

THIS DOESN'T HELP AT ALL!!!!

Oh I see. Thank you!

can you explain it again in proper way

To solve this problem, let's establish the different components of the woman's pay.

Let:
h = number of regular hours worked
o = number of overtime hours worked

Since she earns $10.00 per hour for regular hours, her pay for regular hours worked is 10h.

For overtime hours worked, she is paid 1.5 times her regular salary. Since her regular rate is $10.00 per hour, her overtime rate is 1.5 * $10.00 = $15.00 per hour. Therefore, her pay for overtime hours worked is 15o.

To find the total pay, we sum up the pay for regular hours and pay for overtime hours, and set it equal to $275. So the equation becomes:
10h + 15o = 275

We also know that if she works more than 20 hours in a week, she is paid overtime. So, we have an additional constraint: h + o > 20.

Now, we have a system of two equations:
10h + 15o = 275
h + o > 20

To solve this system and find the number of overtime hours (o), we can use substitution or elimination. Let's use elimination:

First, let's rewrite the second inequality as h > 20 - o.

Substituting this in the first equation:
10(20 - o) + 15o = 275
200 - 10o + 15o = 275
5o = 75
o = 75 / 5
o = 15

Therefore, the woman worked 15 overtime hours that week.