Problem 35 - Prealgebra

Question

JOAnn works in the publicity office at the state university. She is paid \(\$ 14\) an hour for the first 35 hours she works each week and \(\$ 21\) an hour for every hour after that. If she makes \(\$ 574\) one week, how many hours did she work?

Step-by-Step Solution

Answer

JoAnn worked 39 hours.

Step 1: Understand the Problem

JoAnn gets paid $14 per hour for the first 35 hours and $21 for each extra hour. We need to find how many hours in total she worked if she made $574.

Step 2: Determine if the Total Reached is Below or Above Regular Salary

Calculate the amount earned from the first 35 hours: 35 hours * $14/hour = $490. Since $574 is more than $490, JoAnn worked overtime.

Step 3: Calculate Overtime Pay

Find out how much JoAnn earned from overtime by subtracting the regular pay from the total pay: $574 - $490 = $84. This $84 is earned at the overtime rate.

Step 4: Calculate Overtime Hours

Divide the overtime pay by the overtime hourly rate to find overtime hours: $84 / $21/hour = 4 hours.

Step 5: Calculate Total Hours Worked

Add regular hours to overtime hours to get total hours: 35 hours (regular) + 4 hours (overtime) = 39 hours.

Key Concepts

Overtime Pay

Overtime pay is additional compensation that employees earn for working beyond their standard working hours. This is a common practice in many workplaces and serves to compensate employees for their extra time and effort. In JoAnn's case, she earns an overtime rate of $21 per hour for any hours worked beyond the standard 35 hours each week.
Understanding how overtime pay works can help solve problems involving wage calculations. JoAnn's overtime pay was calculated by first determining how much she earned from her regular hours, which totaled $490. Since her total earnings were $574, she made an extra $84 in overtime. The overtime rate of $21 per hour was then used to figure out how many overtime hours she worked, which is found by the formula:

• Overtime Pay = total pay - regular pay
• Overtime Hours = Overtime Pay / Overtime Rate

Hourly Wage

The concept of an hourly wage is the foundation of many wage calculations, especially for employees who work variable hours each week. An hourly wage represents the amount of money paid for each hour of work. For JoAnn, her standard hourly wage is $14 per hour for the first 35 hours.
Calculating total earnings involves multiplying the number of hours worked by the hourly wage. In any given problem-solving scenario, understanding the hourly wage rate is crucial to calculating total pay and identifying how much is earned at regular versus overtime rates. This understanding is not only essential for figuring out total salary, but also for financial planning, and granting insights into how altering hours could affect take-home pay.
When you know how much you earn per hour, you can easily calculate your total earnings from regular hours and compare them against your overtime to understand your total income.

Problem Solving

Problem-solving in wage calculations involves several steps to ensure accurate outcomes. It is important to understand the information provided and identify what is needed to reach a solution. For JoAnn's problem, one must:

• Identify regular and overtime hourly rates
• Calculate how much she earns from regular hours
• Determine if the total earnings suggest overtime
• Calculate any overtime pay and hours
This systematic approach helps in breaking down complicated wage problems into more manageable parts.
In JoAnn's situation, subtracting her regular pay from the total earned helped deduce that she worked overtime. Such problems not only enhance mathematical skills but also provide practical skills applicable in daily life scenarios like budgeting and financial planning. Recognizing each part of the problem and using structured steps ensure the right solution is obtained efficiently.