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Math Applied to Real World

We explore salary-based calculations, overtime, commissions, and investment scenarios using practical examples.

Question 1: Gross Pay Calculation

James earns an annual salary of $21,600. He is paid biweekly and works 40 hours per week. To determine his gross pay per pay period, we calculate the number of biweekly pay periods in a year: 52 weeks ÷ 2 = 26 pay periods. Therefore, his gross pay per pay period is $21,600 ÷ 26 = $831 (rounded to the nearest dollar).

Question 2: Hourly Rate Calculation

James works 40 hours per week. To calculate his hourly rate, we first determine the total hours worked in a year: 40 hours/week × 52 weeks = 2,080 hours. His hourly rate is $21,600 ÷ 2,080 = $10.38/hour.

Question 3: Overtime Calculation

James’s gross pay for one pay period is $1,180. His regular pay is $831, so the difference represents his overtime pay: $1,180 - $831 = $349. Since overtime is paid at double his hourly rate, his overtime hourly rate is $10.38 × 2 = $20.76. To find out how many overtime hours James worked, we divide his overtime pay by the overtime rate: $349 ÷ $20.76 = 17 hours of overtime.

Question 4: Mia’s Total Net Sales

Mia earns a total of $452.75, with a base salary of $375 and a commission of 5% on sales exceeding $7,000. To find her commission earned, subtract her base salary from her total earnings: $452.75 - $375 = $77.75. Next, divide this amount by the commission rate: $77.75 ÷ 0.05 = $1,555, which represents her sales exceeding the quota. Therefore, Mia’s total net sales, including the quota, are $7,000 + $1,555 = $8,555. After deducting sales returns of $250, her net sales amount to $8,305.

Question 5: Investment Calculation

Leo invests $200 per month and buys units at varying prices. The number of units purchased each month is calculated as follows:

  • $200 ÷ $8.75 = 22.86 units
  • $200 ÷ $9.25 = 21.62 units
  • $200 ÷ $10.00 = 19.80 units
  • $200 ÷ $7.85 = 25.48 units

Question 6: GST Calculation

Finally, the cost of a laptop is $1,299.95. To calculate the GST at a rate of 5%, we multiply the cost by 0.05: $1,299.95 × 0.05 = $64.99. If PST is 8%, we add $1,299.95 × 0.08 = $103.99, giving a total tax of $168.98.

These examples demonstrate how to apply practical math skills to real-world financial scenarios, such as salary calculations, overtime pay, commissions, and investments. 

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