Bill Tupper makes $24 per hour for a 40 hour work week....

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atrom9

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Feb 13, 2007
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I think this is the right area for College Algebra, if it isn't I apologize. Here is my problem.

Bill Tupper makes $24 per hour for a 40 hour work week. He earns time and a half for every hour over 40 hours during that one week. If Bill earned $1140 last week, how many overtime hours did he work?

My question is...I am supposed to translate this problem into an equation and then solve. My brother and Sister have shown me how to get the right answer, they just can't show me how to put the problem into an equation. Please if you could show me how to figure out the equation, I would like to see if I can solve the equation. Thank you so much. :oops:
 
r = regular hours (40)
h = hourly wage (24)
f = overtime factor (1.5)
t = total earned (1140)

overtime hours = (t - hr) / (fr) where t >= hr

= (1140 - 24*40) / (1.5 * 24)
 
Bill Tupper makes $24 per hour for a 40 hour work week. He earns time and a half for every hour over 40 hours during that one week. If Bill earned $1140 last week, how many overtime hours did he work?

#1 Name Stuff - Particularly what you are looking for.

"how many overtime hours did he work"

Name that.

x = the number of overtime hours he worked.

#2 Translate the pieces.

"Bill Tupper makes $24 per hour for a 40 hour work week"

That's 40 hr * $24/hr = $960

"He earns time and a half for every hour over 40 hours during that one week."

That's 1.5*$24/hr = $36/hr
Since he worked x hours of overtime, his overtime pay is x*$36/hr

"If Bill earned $1140 last week,"

Let's build his earnings.

$960 + x*$36/hr = $1140

Just one piece at a time. Always thinking about it along the way. The greatest stumbling block often is a desire to see the end from the beginning. Don't do it. Let the notation help you. For example, why did I decide to multiply 40 hr * $24/hr? Did I KNOW that would help me later on? Not necessarily. It was a question that jumped to mind as I was writing. There is no need to follow a single "correct" pathway - particularly since there isn't such a thing. The answer is unique. It doesn't care how you find it.
 
Re: College Algebra: Word Problems

Hello, atrom9!

tkhunny has the best approach.
You can baby-talk your way through the problem . . .

Bill Tupper makes $24 per hour for a 40-hour work week.
He earns time-and-a-half for every hour over 40 hours during that one week.
If Bill earned $1140 last week, how many overtime hours did he work?
Click to expand...

Let \(\displaystyle x\) = number of overtime hours Bill worked.

Then for his first 40 hours, he earned: \(\displaystyle \,24\,\times\,40\:=\:960\) dollars.

For his \(\displaystyle x\) hours of overtime, he earned: \(\displaystyle \,\$36\,\times\,x\:=\:36x\) dollars.

Since his pay was $1140, we have: \(\displaystyle \:960\,+\,36x\:=\:1140\)

. . Now solve for \(\displaystyle x\) . . .

 
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