NavGanitMateby NavGreen Compute, AustraliaBased on Victorian Curriculum Mathematics v2.0
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Percentage change and error

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A sports club in Perth allocates 55 new basketballs and 50 new footballs for use across its training centres. After a season, the club estimates that 11% of the basketballs and 15% of the footballs are no longer usable.

The actual number of unusable basketballs is 6, and the actual number of unusable footballs is 8. Calculate the exact percentage error in the club's estimate of the total number of unusable balls.

Express your answer as a simplified fraction.

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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.
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.

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Worked solution

  1. The club allocated 55 basketballs and 50 footballs. The estimated percentage of unusable basketballs is 11%, and for footballs is 15%. Convert percentages to decimals by dividing by 100: 11% = 0.11, 15% = 0.15.
  2. Calculate the estimated number of unusable basketballs: 55 × 0.11 = 6.05.
  3. Calculate the estimated number of unusable footballs: 50 × 0.15 = 7.5.
  4. Add the estimated unusable balls: 6.05 + 7.5 = 13.55.
  5. The actual number of unusable basketballs is 6, and for footballs is 8. Add these to get the actual total unusable balls: 6 + 8 = 14.
  6. Calculate the absolute error: |13.55 - 14| = 0.45.
  7. Calculate the percentage error using the formula: (absolute error / actual value) × 100. Substitute values: (0.45 / 14) × 100.
  8. First compute 0.45 / 14 = 45/1400 = 9/280.
  9. Multiply by 100: (9/280) × 100 = 900/280.
  10. Simplify 900/280: divide numerator and denominator by 20 to get 45/14.
  11. Express as a simplified fraction: 45/14 is already in simplest form. The percentage error is 45/14 %.
  12. The exact percentage error in the club's estimate is 45/14 %, which is the simplified fraction required.

Reference answer: 45/14 %

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