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

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A library in Brisbane purchases 61 copies of a new mathematics textbook for a total cost of $17 per book. The library applies a 15% markup on the cost price to cover administrative expenses and ensure a profit.

Later, during a back-to-school promotion, the library offers a 10% discount on the marked-up price.

What is the exact final sale price per textbook, in Australian dollars, expressed as a single fraction?

Concept illustrations

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A quarter is 25 percent. One of four equal parts is 25/100. For a whole of 80, each part is 20.1 of 4 equal parts
One of four equal parts is 25/100. For a whole of 80, each part is 20.
Compare the increase with the original. A price grows from 80 to 100. The added 20 is one quarter of the original 80: a 25% increase. Bar lengths share the same scale.BeforeAfter80802020 ÷ 80 × 100% = 25%
A price grows from 80 to 100. The added 20 is one quarter of the original 80: a 25% increase. Bar lengths share the same scale.

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Explanation

Worked solution and answer (click to reveal)

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Worked solution

  1. The library purchases 61 textbooks at $17 each. The total cost is 61 × 17 = $1037.
  2. The library applies a 15% markup on the cost price. Markup amount = 15% of $17 = (15/100) × 17 = 0.15 × 17 = $2.55.
  3. The marked-up price per book is $17 + $2.55 = $19.55.
  4. During the promotion, a 10% discount is applied to the marked-up price. Discount amount = 10% of $19.55 = (10/100) × 19.55 = 0.10 × 19.55 = $1.955.
  5. The final sale price per book is $19.55 - $1.955 = $17.595.
  6. Convert $17.595 to a fraction. First, write as 17595/1000.
  7. Simplify 17595/1000 by dividing numerator and denominator by 5: 3519/200.
  8. Check if 3519 and 200 have any common factors. 200 = 2^3 × 5^2. 3519 is odd, so not divisible by 2. 3519 ends in 9, not 0 or 5, so not divisible by 5. Thus, 3519/200 is in simplest form.
  9. The final sale price per textbook is 3519/200 dollars.
  10. Verify the calculation: 15% of 17 = 2.55 → 17 + 2.55 = 19.55. 10% of 19.55 = 1.955 → 19.55 - 1.955 = 17.595. 17.595 = 17595/1000 = 3519/200. Correct.
  11. The exact final sale price per textbook is 3519/200 AUD.
  12. The answer is a single fraction, as required.

Reference answer: 3519/200

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