NavGanitMateby NavGreen Compute, AustraliaBased on Australian Curriculum: Mathematics v9.0
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Proportion, rates and scale modelling

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A sports equipment supplier in Perth is allocating basketballs and tennis balls to schools using a proportional model based on student enrolment. For every 57 students, 42 basketballs are allocated.

If a school has 1140 students, what is the exact number of basketballs allocated? Use direct proportion to determine the answer.

Concept illustrations

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A one-to-one-hundred length scale. At scale 1:100, a 3 cm drawing length represents 300 cm = 3 m. The two bars are symbolic and not shown at a 1:100 size ratio.Drawing: 3 cmReal: 300 cm = 3 m×100
At scale 1:100, a 3 cm drawing length represents 300 cm = 3 m. The two bars are symbolic and not shown at a 1:100 size ratio.
Two red counters for every three blue counters. Red:blue = 2:3. There are 5 counters in all, so the red fraction of the whole is 2/5.RedRedBlueBlueBlue2 red : 3 blue · 5 counters in all
Red:blue = 2:3. There are 5 counters in all, so the red fraction of the whole is 2/5.

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Worked solution

  1. The problem states that for every 57 students, 42 basketballs are allocated. This is a direct proportion relationship between students and basketballs.
  2. The school has 1140 students. We need to find how many basketballs are allocated based on the given ratio.
  3. Set up the proportion: 42 basketballs / 57 students = x basketballs / 1140 students.
  4. Cross-multiply to solve for x: x = (42 × 1140) / 57.
  5. First, calculate 42 × 1140. Break it down: 42 × 1000 = 42,000; 42 × 140 = 42 × 100 + 42 × 40 = 4,200 + 1,680 = 5,880. Total = 42,000 + 5,880 = 47,880.
  6. Now divide 47,880 by 57. Perform the division: 57 × 800 = 45,600. Subtract: 47,880 - 45,600 = 2,280.
  7. Now divide 2,280 by 57. 57 × 40 = 2,280. So 800 + 40 = 840.
  8. Therefore, x = 840 basketballs.
  9. Check: 57 students → 42 basketballs. 1140 ÷ 57 = 20. So 20 × 42 = 840. The result is consistent.
  10. The allocation is proportional and the calculation is exact. No rounding is needed.
  11. The school with 1140 students is allocated exactly 840 basketballs.
  12. Final answer confirmed by direct proportion and verification via division and multiplication.

Reference answer: 840 basketballs

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