Answer:
$11.20 per hour
Step-by-step explanation:
You want to know Julio's base pay when he worked 45 hours and earned $554.40, including a 30% premium for hours over 30.
<h3>Setup</h3>
For pay p per hour for h hours, Julio's pay is ...
pay = p·h +0.3p·(h -30)
Using the given values of pay and hours, we have ...
554.40 = p(45) +0.3p(45 -30) . . . . . . . equation with given values
554.40 = 45p +4.5p
554.40 = 49.5p . . . . . . simplified equation
<h3>Solution</h3>
Dividing by the coefficient of p gives ...
p = $554.40/(49.5 h) = $11.20/h
Julio's normal hourly rate is $11.20 per hour.
<h3>Reasonableness check</h3>
At this rate, 45 hours of straight time would give pay of about ...
$11.20 h × 45/h = $504
His overtime pay is for 0.3(45 -30) = 4.5 hours, which is 10% more than his 45 straight time hours. That adds 10% to the pay, making the total ...
$504 +50.4 = $554.40 . . . . . matching the given amount
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<em>Additional comment</em>
The equation including the factor (h-30) is only valid for values of h that are at least 30. If Julio works 30 or fewer hours, his pay is ...
pay = ph . . . . . where p = 11.20
Effectively, the equation for pay is a piecewise-defined function. In this problem, we're only concerned with the piece that applies for h>30.
