NavGanitMateby NavGreen Compute, AustraliaBased on Australian Curriculum: Mathematics v9.0
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Exploring formulas

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A sports equipment supplier is allocating basketballs to schools using the formula: number of basketballs = (71 × 86) ÷ 100. What is the exact number of basketballs allocated?

Express your answer as a simplified fraction if necessary.

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Replace x with its given value. For x = 4, the expression 2x + 3 becomes 2 × 4 + 3 = 11.2x + 3x = 4→2 × 4 + 3Substitute→11Evaluate
For x = 4, the expression 2x + 3 becomes 2 × 4 + 3 = 11.
Keep both sides balanced. The level beam represents equality, not measured weights. Subtract 6 from both sides of x + 6 = 14 to leave x = 8.x + 614−6−6x = 8
The level beam represents equality, not measured weights. Subtract 6 from both sides of x + 6 = 14 to leave x = 8.

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Explanation

Worked solution and answer (click to reveal)

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Worked solution

  1. The formula given is: number of basketballs = (71 × 86) ÷ 100.
  2. First, calculate the product of 71 and 86.
  3. Use multiplication: 71 × 86.
  4. Break 86 into 80 + 6 for easier calculation: 71 × 80 = 5680, and 71 × 6 = 426.
  5. Add the two parts: 5680 + 426 = 6106.
  6. Now divide 6106 by 100: 6106 ÷ 100.
  7. Dividing by 100 moves the decimal point two places left: 6106 ÷ 100 = 61.06.
  8. The result is 61.06, but the question asks for the exact number of basketballs.
  9. Since basketballs are whole items, the number must be an integer.
  10. 61.06 is not a whole number, so we must determine whether to round up or down.
  11. The formula uses division by 100, which suggests a percentage-based allocation. However, the result must be a whole number of basketballs.
  12. The exact value of (71 × 86) ÷ 100 is 6106/100, which simplifies to 3053/50. Since 3053 ÷ 50 = 61.06, and basketballs cannot be fractional, the supplier must allocate 61 basketballs (as partial basketballs are not possible).

Reference answer: 61

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