Math Problem Statement

A salesperson earns a $250 per week retainer, plus 2% commission on the first $1000 of sales and 1.5% on the remainder. What is their total income for a week in which sales are $18,000?

Solution

I see you've uploaded an image containing several word problems focused on salaries, commissions, and interest rates. Let me extract and work on each question in detail. Here's a breakdown of the math problems based on the image:

Questions:

  1. Salesperson's Total Income:

    • A salesperson earns $250 per week, plus 2% commission on $1000 of sales and 1.5% on the remainder. What is their total income for a week in which sales are $18,000?
  2. New Job Selling Mobile Phones:

    • Jennifer starts a new job selling mobile phones. She is paid a commission of 17.5% of all sales. What value of sales must she make to receive a commission of $1400?
  3. Phillipa's Annual Salary:

    • Phillipa is paid an annual salary of $71,500.
      1. Calculate Phillipa's gross weekly income.
      2. Her union fees are 1.15% of her gross salary. How much does she pay annually in union fees?
  4. Chief Financial Officer's Annual Salary:

    • A CFO of a major firm in Sydney earns a base salary of $4.25 million. If the firm's share price increases, the CFO earns an additional $1.5 million. If the share price decreases, the CFO's pay is reduced by $900,000. Calculate:
      • The CFO's total salary if the share price rises.
      • The CFO's total salary if the share price falls.
  5. Hourly Wage and Weekly Earnings:

    • A chef works a total of 40 hours per week and is paid $20 per hour. For any hours over 40, the chef is paid 1.5 times the normal hourly rate. Calculate:
      • The chef's weekly wage if they work 50 hours.
  6. Chief Executive Pay:

    • The CEO of a firm earns $2.5 million in fixed pay and receives a 50% bonus if the firm's earnings increase by 25%. If the firm's earnings increase by 30%, how much is the CEO's total compensation?
  7. Simple Interest on a Loan:

    • A simple interest loan of $8000 is repaid over 4 years. The interest is $2920. What is the interest rate charged?

I can start solving these problems one by one. Would you like me to begin with the first question on the salesperson's total income?

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Math Problem Analysis

Mathematical Concepts

Percentages
Commissions
Basic Arithmetic

Formulas

Total Income = Weekly Retainer + Commission on First Portion of Sales + Commission on Remainder of Sales
Commission on First Portion = First Portion of Sales * Commission Rate
Commission on Remainder = Remainder of Sales * Remainder Commission Rate

Theorems

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Suitable Grade Level

Grades 9-10