Question

Julio is paid 1.3 times his normal hourly rate for each hour he works over 30 hours in a week. Last week he worked 45 hours and earned $554.40.
Enter and solve an equation to find Julio's normal hourly rate, r. Complete the explanation how you know that your answer is reasonable.

(Mostly need the equation)

Answer 1

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.

Setup

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

Solution

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.

Reasonableness check

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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Additional comment

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.

Answer 2

Julio's normal hourly rate is gotten as; r = $11.20 per hour.

How to find rate of work?

Let pay be p per hour.

Let number of hours be h.

Thus, Julio's pay is expressed as;

p*h + 0.3p(h - 30)

This is because he is paid 1.3 times his normal hourly rate for each hour he works over 30 hours.

We are told that last week, he worked 45 hours and earned $554.40. Thus, this can be expressed as;

554.40 = p(45) + 0.3p(45 - 30)

554.40 = 45p +4.5p

554.40 = 49.5p

Divide each side by 49.5 to get;

p =  $11.20/h

Thus, we can conclude that Julio's normal hourly rate is r = $11.20 per hour.

Read more about Rate of Work proportion at; brainly.com/question/10520217

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