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The Rockville Employment Agency just placed Howard Jacobson in a job as a junior pharmacist. The job pays \(\$ 51.2 \mathrm{K}\) . The agency fee is equal to 40\(\%\) of the first three weeks' pay. a. What is Howard's weekly salary to the nearest cent? b. What will Howard earn during the first three weeks? c. How much must Howard pay the employment agency to the nearest dollar?

Short Answer

Expert verified
a. The weekly salary for Howard is approximately \$984.62. b. Howard will earn approximately \$2953.85 during the first three weeks. c. Howard needs to pay approximately \$1182 to the employment agency.

Step by step solution

01

Identify the yearly and weekly salary

Howard earns \$51.2K per year. To find the weekly salary, simply divide the yearly salary by the total number of weeks in a year. Since there are 52 weeks in a year, Howard's weekly salary would be \(\$51.2K / 52\).
02

Calculate the three weeks' earning

To find the total earnings for the first three weeks, multiply the weekly salary by three. This should be \(3 * (yearly salary / 52)\).
03

Calculate the employment agency's fee

The employment agency charges 40% of the first three weeks' pay. To find this, simply compute for 40% of the total three weeks' earnings. This should be \(0.4 * (3 * (yearly salary / 52))\)

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Salary Calculation
Understanding how to calculate your weekly salary is an essential skill, especially when starting a new job. In this example, Howard Jacobson's yearly salary is \(51,200, often abbreviated as \)51.2K. To find the weekly salary, you need to divide the annual salary by the number of weeks in a year. Let’s walk through this step-by-step.
Firstly, take the yearly salary: \(51,200. Divide this number by 52, the number of weeks in a year. This calculation will give you Howard's weekly salary. Mathematically, it looks like this:
\[\text{Weekly Salary} = \frac{\\)51,200}{52}\]Calculating the above will give you the exact weekly salary to the nearest cent. It's crucial because it helps determine not only weekly cash flow but also aids in planning budgets and finances effectively.
  • Yearly Salary: \(51,200
  • Weeks per Year: 52
  • Weekly Salary Calculation: \)51,200 ÷ 52
Employment Agency Fee
Employment agencies often charge fees for their services, which can affect the first few paychecks or earnings. In this scenario, the Rockville Employment Agency charges a fee equivalent to 40% of Howard's first three weeks' pay. Understanding how this fee is calculated is essential for budgeting during the initial period of employment.
To calculate the agency fee, first determine the total earnings for the first three weeks—multiply the weekly salary by three. Let's denote Howard's weekly salary as \( \text{weekly salary} \).
\[\text{Three Weeks' Earnings} = 3 \times \text{weekly salary}\]Next, apply the 40% fee formula to this amount:
\[\text{Agency's Fee} = 0.4 \times (3 \times \text{weekly salary})\]This fee impacts how much Howard effectively takes home in his first pay periods. It is crucial to factor such fees into financial planning following a placement through an employment agency.
  • Three Weeks Earnings = Weekly Salary × 3
  • Agency Fee = 40% of the Three Weeks Earnings
Weekly Earnings
To understand potential income, you need to calculate what you will earn over a set period—in this case, three weeks. This calculation helps in financial planning, ensuring short-term expenses are covered and align with income.
For Howard, calculating his earnings for three weeks involves knowing his weekly salary, which we've identified previously. Simply multiply this weekly salary amount by three:
\[\text{Total Earnings for Three Weeks} = 3 \times \text{Weekly Salary}\]This total helps Howard understand what he can expect to take home before any deductions, such as the employment agency fee. It's also a useful figure for setting financial goals or planning for upcoming expenses during the employment transition period.
  • Weekly Salary: Calculated previously
  • Earnings over Three Weeks: Weekly Salary × 3

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