Bruce earns 1.5 times his normal hourly rate for each hour he works after 40 hours in a week. He worked 53 hours this week and earned $833. What is his normal hourly rate?
Let x = hourly rate and
1.5x = overtime rate.
--------------------
40*x + 13*1.5x = 833
Solve for x.
40(x)+13(1.5x)=833
=40x+20x=833
=60x=833
x needs to be isolated, so divide 60 from 833
x=833/60
x=14
hourly rate =$14.00
overtime rate=1.5(14)=$21.00
Where did you guys get the 13 from?
53-40 = 13
To determine Bruce's normal hourly rate, we can follow these steps:
1. Calculate the number of hours Bruce worked after the initial 40 hours: 53 hours - 40 hours = 13 hours.
2. Calculate the additional pay Bruce received for those extra 13 hours: 13 hours x (1.5 times normal rate).
3. Subtract the additional pay from his total earnings to find his earnings for the first 40 hours: $833 - additional pay.
4. Divide the earnings for the first 40 hours by the number of hours worked to find Bruce's normal hourly rate: earnings for first 40 hours / 40 hours.
Let's calculate it step by step:
1. Bruce worked for 13 hours after the initial 40 hours.
2. The additional pay for those 13 hours is: 13 hours x (1.5 times normal rate) = 13 hours x 1.5 = 19.5 times the normal rate.
3. Subtracting the additional pay from his total earnings: $833 - $19.5 times the normal rate = $833 - $19.5 times the normal rate.
4. We need to find the earnings for the first 40 hours, so we subtract the additional pay from the total earnings: $833 - $19.5 times the normal rate = $813.5 times the normal rate.
5. Lastly, we divide the earnings for the first 40 hours by the number of hours worked to find Bruce's normal hourly rate: $813.5 times the normal rate / 40 hours.
Hence, to determine Bruce's normal hourly rate, calculate $813.5 times the normal rate divided by 40 hours.