NavGanitMateby NavGreen Compute, AustraliaBased on Australian Curriculum: Mathematics v9.0
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Percentages and financial modelling

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In Perth, a small business owner purchases 150 custom-designed notebooks for a total cost of $2250. To cover operating expenses and ensure a profit, the owner applies a 35% markup on the total cost before selling.

During a promotional event, the owner offers a 20% discount on the marked-up total price. What is the exact final total selling price for all 150 notebooks, in Australian dollars?

Express your answer as a single exact fraction.

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Worked solution

  1. The total cost for 150 notebooks is $2250. This is the base cost before any markup or discount.
  2. A 35% markup is applied to the total cost. To calculate the markup amount, convert 35% to a decimal by dividing by 100: 35 / 100 = 0.35.
  3. Multiply the base cost by the markup decimal: 2250 * 0.35 = 787.50. This is the amount of markup.
  4. Add the markup to the base cost to find the marked-up price: 2250 + 787.50 = 3037.50. This is the price before any discount.
  5. A 20% discount is applied to the marked-up price. Convert 20% to a decimal: 20 / 100 = 0.20.
  6. Calculate the discount amount: 3037.50 * 0.20 = 607.50.
  7. Subtract the discount from the marked-up price to get the final selling price: 3037.50 - 607.50 = 2430.00.
  8. The final total selling price is $2430.00. Express this as a fraction: 2430 = 2430/1.
  9. Simplify the fraction 2430/1. Since 2430 is an integer, the simplest fractional form is 2430/1.
  10. Verify the calculation using fractions to preserve exactness. The 35% markup is 35/100 = 7/20. The marked-up price is 2250 * (1 + 7/20) = 2250 * 27/20.
  11. Calculate 2250 * 27 / 20: 2250 / 20 = 112.5; 112.5 * 27 = 3037.5. This matches the decimal result.
  12. Apply the 20% discount as a multiplier: 1 - 20/100 = 0.80 = 4/5. Final price = 3037.5 * 4/5 = (3037.5 * 4) / 5 = 12150 / 5 = 2430. The exact final total selling price is 2430/1.

Reference answer: 2430/1

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