NavGanitMateby NavGreen Compute, AustraliaBased on Australian Curriculum: Mathematics v9.0
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Relationships between variables

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A school in Sydney orders 93 pens and 37 notebooks for the new term. The cost of each pen is $1.75 and each notebook is $3.25.

The total cost of the order is modelled by a linear relationship between the number of pens and notebooks. What is the total cost of the order?

Express your answer as an exact fraction in Australian dollars.

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Association between paired values. Authored example pairs show a positive association: larger x tends to accompany larger y. A scatterplot alone cannot establish causation. Axes show arbitrary numerical units.xyPaired observations
Authored example pairs show a positive association: larger x tends to accompany larger y. A scatterplot alone cannot establish causation. Axes show arbitrary numerical units.
A straight-line relationship. Illustration: y = x + 1. Each unit right adds one unit up; the y-intercept is 1.-2-2-1-111223344xy
Illustration: y = x + 1. Each unit right adds one unit up; the y-intercept is 1.

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Worked solution and answer (click to reveal)

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Worked solution

  1. The school orders 93 pens and 37 notebooks. The cost per pen is $1.75 and per notebook is $3.25. We need to find the total cost using a linear relationship between the number of pens and notebooks.
  2. The total cost is the sum of the cost of pens and the cost of notebooks. This is a linear relationship: total cost = (number of pens × cost per pen) + (number of notebooks × cost per notebook).
  3. Convert the cost per pen to a fraction: $1.75 = 175/100 = 7/4 dollars.
  4. Convert the cost per notebook to a fraction: $3.25 = 325/100 = 13/4 dollars.
  5. Calculate the total cost for pens: 93 × (7/4) = (93 × 7) / 4 = 651 / 4.
  6. Calculate the total cost for notebooks: 37 × (13/4) = (37 × 13) / 4 = 481 / 4.
  7. Add the two costs: (651 / 4) + (481 / 4) = (651 + 481) / 4 = 1132 / 4.
  8. Simplify the fraction: 1132 ÷ 4 = 283. So, 1132 / 4 = 283.
  9. The total cost is $283. As an exact fraction, this is 283/1.
  10. Check: 93 × 1.75 = 162.75, 37 × 3.25 = 120.25, sum = 162.75 + 120.25 = 283.00. The calculation is correct.
  11. The total cost of the order is $283, which as an exact fraction is 283/1 Australian dollars.
  12. The answer is expressed as an exact fraction in Australian dollars, as required.

Reference answer: 283/1

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