NavGanitMateby NavGreen Compute, AustraliaBased on Australian Curriculum: Mathematics v9.0
← Back to practice

Rational numbers and financial modelling

Wide tables scroll horizontally. For detailed working, you may prefer a larger screen.

Required skills (click to reveal)

A community garden in Brisbane is planning to build a rectangular vegetable plot with a length of 39 metres and a width of 36 metres. The garden group has allocated $3,600 for fencing and soil.

The fencing costs $12.50 per metre, and the soil costs $2.40 per square metre.

What is the exact percentage profit made on the total expenses if the garden group receives $4,200 in donations for the project? (Profit = (Revenue - Expenses) / Expenses × 100, and the answer must be expressed as a simplified fraction.)

Rectangle measurementsLength 39 metres; width 36 metres39 metres36 metres
Measurements from the question · not to scale.
Concept illustrations

These are separate worked examples of related concepts, not a diagram of this question. Their values and dimensions do not describe your question.

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.
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.

Press Start when ready. Time includes time spent in another tab. Submit your answer before opening a help panel for a timed rank.

00:00
0 wordsOnly your numerical final answer or selected MCQ option is checked. Scratch working is not graded.

Report a problem or suggest an improvement

My notes — optional, not graded 0 words

Notes and scratch working stay in this browser and are linked to this question version. They are not graded or included in feedback. On shared devices, other people using this browser may see them.

For this question only. Your full notebook is on the dashboard.

Notes save in this browser. Download a copy to keep them elsewhere.

Report a problem or suggest an improvement

Your observations help improve this question. You can report an issue or recommend a better explanation, visual or experience.

0 words

The report includes your message and question/version details. Saved profile details, answers, notes and attempt history are not automatically attached. Leave out names and contact details, and check screenshots for personal information and embedded metadata.

Attachments may contain personal information. Review them before sharing. Logs collect only event codes and timestamps after you enable them. Download the ZIP to keep a copy, then attach it to an email if you choose.

Formula and explanation (click to reveal)

Opening this before your first submission makes the attempt practice only.

Formula

Explanation

Worked solution and answer (click to reveal)

Opening this before your first submission makes the attempt practice only.

Worked solution

  1. The rectangular vegetable plot has a length of 39 m and a width of 36 m. The fencing cost is $12.50 per metre, and the soil cost is $2.40 per square metre. The total donation received is $4,200. We need to calculate the percentage profit using the formula: Profit = (Revenue - Expenses) / Expenses × 100.
  2. First, calculate the perimeter of the rectangular plot to determine the fencing cost. Perimeter = 2 × (length + width) = 2 × (39 + 36) = 2 × 75 = 150 metres.
  3. Fencing cost = perimeter × cost per metre = 150 × $12.50. Calculate: 150 × 12.50 = 150 × (12 + 0.50) = (150 × 12) + (150 × 0.50) = 1800 + 75 = $1,875.
  4. Next, calculate the area of the plot for soil cost. Area = length × width = 39 × 36. Compute: 39 × 36 = (40 - 1) × 36 = 40×36 - 1×36 = 1440 - 36 = 1,404 square metres.
  5. Soil cost = area × cost per square metre = 1,404 × $2.40. Compute: 1,404 × 2.40 = 1,404 × (2 + 0.40) = (1,404 × 2) + (1,404 × 0.40) = 2,808 + 561.60 = $3,369.60.
  6. Total expenses = fencing cost + soil cost = $1,875 + $3,369.60 = $5,244.60.
  7. Revenue = $4,200 (donations received). Since revenue ($4,200) is less than expenses ($5,244.60), this results in a loss, not a profit.
  8. Calculate profit (which is negative): (Revenue - Expenses) / Expenses = (4,200 - 5,244.60) / 5,244.60 = (-1,044.60) / 5,244.60.
  9. Simplify the fraction: -1,044.60 / 5,244.60. Multiply numerator and denominator by 10 to eliminate decimals: -10,446 / 52,446.
  10. Simplify the fraction by dividing numerator and denominator by 6: -10,446 ÷ 6 = -1,741; 52,446 ÷ 6 = 8,741. So, -1,741 / 8,741. Check if this fraction can be simplified further. GCD of 1,741 and 8,741 is 1 (verified via Euclidean algorithm). So, the simplified fraction is -1,741 / 8,741.
  11. Convert to percentage: (-1,741 / 8,741) × 100 = -174,100 / 8,741 ≈ -19.92%. But the question asks for the exact percentage profit as a simplified fraction. So, the profit as a fraction of expenses is -1,741 / 8,741. Therefore, the percentage profit is (-1,741 / 8,741) × 100 = -174,100 / 8,741. This fraction cannot be simplified further. Express as a simplified fraction: -174100 / 8741.
  12. The result is a loss, so the profit is negative. The exact percentage profit is -174100/8741. This is the simplified fraction form. The final answer is expressed as a simplified fraction.

Reference answer: -174100/8741

Alternative methods (click to reveal)

Shortcuts are shown only when applicable. Check the conditions before using one.

Earlier attempts for this question

#Date / timeYour answerResultSecondsHelp revealedRank
History stays in this browser when storage is available. Export it to your shared Drive folder and import it on another computer.
Worksheet details

Naming pattern: Topic_Grade_Complexity_YYYYMMDD_HH24MISS.html

Validation compares your answer with the generated reference. The model's reference can be wrong. Time ranks use an estimated student solving time, not a measured benchmark or a comparison with other students. An incorrect answer receives no speed rank.

NavGanitMate privacy & saved work

Saved in this browser. Your profile preferences, answers, practice history and notes are stored here when browser storage is available. They are not automatically uploaded to our servers. People sharing this browser may see saved work; changing the learner name does not create a separate private account. A nickname is enough.

Keep copies of important work. Clearing browser data, private browsing or changing browser or device can mean losing saved work. Download notes and export history separately. Downloads are copies of the selected content, not a complete account backup; not every format can be imported to restore your work. Keep these files somewhere private.

Visiting the website. Cloudflare helps deliver and protect this site and processes connection information such as IP addresses and requested pages. Server error logs may also contain request details. Security features may use cookies. This is separate from your browser-saved learning records. Cloudflare privacy information.

A parent-connection reminder uses a local list of up to five completed question IDs for this browser profile and a tab-session dismissal marker. Reminder activity is not uploaded and practice remains available.

Sharing feedback is your choice. A report includes your message and question/version details. Your saved profile, answers and notes are not automatically attached. Files you select can reveal personal details or contain embedded metadata: check and redact them before sharing. Diagnostic event codes and timestamps are included only after you enable logging. Sending email shares your message and attachments with the recipient and email providers. A download alone sends nothing to us. Website feedback delivery may be unavailable; only a confirmed receipt indicates it was received.