Math Problem Statement

Her annual salary is $72800. A- calculate her weekly wage. B- holiday loading is calculated at 17.5% of four weeks pay, calculate her holiday loading. C- employer Increased her annual salary by 1%. What is the new annual salary. D- the increase in her annual salary is compensation for removing holiday loading. Explain why she is worse off financially with 1% increase.

Solution

Let's break this problem down step by step:

A. Calculate her weekly wage.

To calculate her weekly wage, divide her annual salary by the number of weeks in a year (52 weeks):

Weekly wage=7280052=1400\text{Weekly wage} = \frac{72800}{52} = 1400

So, her weekly wage is $1,400.


B. Calculate her holiday loading.

Holiday loading is 17.5% of four weeks' pay. First, calculate her four weeks' pay:

4 weeks’ pay=4×1400=56004 \text{ weeks' pay} = 4 \times 1400 = 5600

Now, calculate 17.5% of this amount:

Holiday loading=0.175×5600=980\text{Holiday loading} = 0.175 \times 5600 = 980

So, her holiday loading is $980.


C. Employer increased her annual salary by 1%. What is the new annual salary?

To calculate the new salary after a 1% increase:

New salary=72800+(0.01×72800)=72800+728=73528\text{New salary} = 72800 + (0.01 \times 72800) = 72800 + 728 = 73528

So, her new annual salary is $73,528.


D. Why is she worse off financially with the 1% increase?

With the 1% salary increase, her new annual salary is $73,528, but the increase ($728) is less than what she was receiving as holiday loading ($980).

To explain more clearly:

  • Original compensation: $72,800 salary + $980 holiday loading = $73,780 total.
  • After the increase: $73,528 (without holiday loading).

Thus, with the 1% salary increase and the removal of holiday loading, her total compensation has decreased from $73,780 to $73,528, meaning she is $252 worse off.


Summary of answers:

  • A. Weekly wage = $1,400
  • B. Holiday loading = $980
  • C. New annual salary = $73,528
  • D. She is worse off by $252 because the 1% increase does not compensate for the removal of the holiday loading.

Would you like more details on any part of this? Here are 5 related questions to expand on this:

  1. What is the equivalent monthly salary for her original annual salary of $72,800?
  2. How much would her holiday loading be if her weekly wage increased to $1,500?
  3. What would her salary be if her employer offered a 2% raise instead of 1%?
  4. If her new annual salary was $75,000, would she be better or worse off compared to having holiday loading?
  5. What percentage increase in salary would exactly match the amount of holiday loading she received?

Tip: Always compare total compensation (salary + benefits) to understand the true financial impact of a raise or change in benefits.

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Math Problem Analysis

Mathematical Concepts

Percentage Calculation
Salary Calculation
Holiday Loading

Formulas

Weekly wage = Annual salary ÷ 52
Holiday loading = 0.175 × (4 × Weekly wage)
New salary = Annual salary + (0.01 × Annual salary)

Theorems

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Suitable Grade Level

Grades 10-12