NavGanitMateby NavGreen Compute, AustraliaBased on Victorian Curriculum Mathematics v2.0
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Financial modelling with percentages

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A community garden in Adelaide is redesigning its flower bed layout. The garden committee decides to increase the area allocated for native wildflowers by 31% to support local pollinators.

The original area for wildflowers is 51 square metres. What is the exact new area of the wildflower section after the increase?

Express your answer as an exact fraction.

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Explanation

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Worked solution

  1. The original area for native wildflowers is 51 square metres.
  2. The garden committee plans to increase this area by 31%. To apply a percentage increase, convert 31% to a decimal by dividing by 100: 31 ÷ 100 = 0.31.
  3. Calculate the increase in area: 51 × 0.31 = 15.81 square metres.
  4. Add the increase to the original area to find the new total area: 51 + 15.81 = 66.81 square metres.
  5. Convert 66.81 to a fraction. First, write 66.81 as 6681/100.
  6. Simplify 6681/100 by checking for common factors. The greatest common divisor (GCD) of 6681 and 100 is 1, so the fraction is already in simplest form.
  7. Alternatively, express the increase as a fraction: 31% = 31/100.
  8. The new area is the original area multiplied by (1 + 31/100) = 131/100.
  9. Multiply 51 by 131/100: (51 × 131) / 100.
  10. Calculate 51 × 131: 51 × 130 = 6630, and 51 × 1 = 51, so 6630 + 51 = 6681.
  11. So, the new area is 6681/100 square metres.
  12. The exact new area of the wildflower section is 6681/100 square metres.

Reference answer: 6681/100 square metres

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