SOLUTION: Leigh is paid time-and-a-half for hours worked in excess of 40 hours and double-time for hours on Sunday. If Leigh had gross weekly wages of $456 for working 50 hours, 4 of which w
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Question 1198947: Leigh is paid time-and-a-half for hours worked in excess of 40 hours and double-time for hours on Sunday. If Leigh had gross weekly wages of $456 for working 50 hours, 4 of which were on Sunday, what us her regular hourly rate?
My Set Up:
Hours worked = 40 + 10 + 4
Overtime: 14
Hourly Wage = 40x
14(1.5x + 2x)
Salary = 40x + 10(1.5x) + 4(2x), where 2x = double-time
Equation:
40x + 10(1.5x) + 4(2x) = 456
1. Is the set up correct?
2. How is this problem solved without algebra?
You can put this solution on YOUR website! w, hourly rate normally not larger than for 40 hours in the week
1.5w, hourly rate for time larger than 40 hours
2w, rate on Sundays
Gross $456
50 hours worked
4 of them Sunday
-
This means 4 hours Sunday, 6 hours overtime, 40 hours regular time.
Why you would want to solve without algebra is not clear. Unknown quantity is the regular hourly rate.
1. Your idea is right, but you aren't interpreting the given information correctly. She worked a TOTAL of 10 hours of overtime, of which 4 hours were on Sunday. So she had 4 hours of overtime at double pay and 6 hours (not 10) of overtime at time-and-a-half.
Your equation should be
40x+6(1.5x)+4(2x)=456
2. The algebra simply puts in formal mathematical language what the problem tells you.
To solve the problem without algebra, you can figure that the 4 hours at double pay are worth 4*2=8 regular hours, and the 6 hours at time-and-a-half are worth 6*1.5=9 regular hours; so in terms of regular hours she worked 40+8+9 = 57 hours. Then use ordinary arithmetic to divide her pay of $456 by 57 to find that her regular hourly rate is $8.
You can put this solution on YOUR website!
Let be the base wage rate in $/hr
Let be the # weekly hours worked up to
Let be the # Sunday hours worked
Let be the # other overtime hours worked
If Leigh worked hours, of which were on Sunday, then
where
=>
Given:
multiplier for hours is
multiplier for hours is
multiplier for hours is
let be the base wage rate in $/hr, then
her regular hourly rate is $
(