Understand the idea.
Compare what the choice really provides
Compare purchases that meet the same need. Check the quantity required, the total to pay and the budget. A larger pack may cost less per item while still costing more money than you have available.
Price is only one stated consideration. Durability, waste, delivery and usefulness can affect the choice. Explain these trade-offs using the information supplied, without inventing a money value for a benefit or cost that has not been measured.
Test a possible extra cost
A risk is an uncertain event that could change a plan. Work out a supplied extra fee or alternative cost before making the comparison. Add a one-off fee once, and a cost per use for every required use.
State the assumptions supporting the result. A reusable item is cheaper over several uses only if it lasts and any refills are included correctly. A cost comparison can be exact even when weather or other non-price factors still affect the final choice.
See the method in action.
Worked example 1
A reusable bottle costs 12 dollars. A disposable bottle costs 2 dollars each time. Compare the costs for ten uses, assuming refills for the reusable bottle are free.
Worked solution
- 1
Find the disposable cost for ten uses.
Each of the ten uses requires a separate two-dollar bottle.
- 2
Find the reusable cost for the same uses.
The bottle is bought once and the question says refills are free.
- 3
Compare the total costs.
The reusable bottle costs eight dollars less for ten uses.
- 4
Check the assumptions.
This conclusion assumes the reusable bottle lasts for all ten uses and no refill fee is charged.
The reusable bottle is 8 dollars cheaper under the stated assumptions.
Worked example 2
A group chooses between the two trips shown. If the park also needs a 5-dollar shelter booking, compare final costs.
| Cost in dollars | Museum | Park |
|---|---|---|
| Entry | 12 | 0 |
| Transport | 18 | 15 |
| Lunch | 6 | 6 |
Worked solution
- 1
Total the museum costs.
Entry, transport and lunch all contribute to the museum total.
- 2
Total the park costs including the booking.
The extra shelter fee belongs to the park option and is paid once.
- 3
Calculate the cost difference.
The park remains ten dollars cheaper after including the shelter.
- 4
Interpret the comparison.
The totals compare cost; weather and suitable activities may still influence which trip the group prefers.
Museum 36 dollars; park 26 dollars; difference 10 dollars.
Try it yourself.
Check your understanding
You need ten pens and have 6 dollars. A pack of ten costs 5 dollars; a pack of twenty costs 8 dollars. Which can you buy?
Show answer & reasoning
The pack of ten.
The ten-pen pack meets the need and costs dollars, within the -dollar budget. The twenty-pen pack costs dollars, which exceeds the available money.
Keep practising
6 worksheet questions · 12 marks
Read the questions online
- A 15-dollar bottle can be used twelve times with free refills. Single-use bottles cost 2 dollars each. How much is saved by choosing the reusable bottle for twelve uses?2 marks
- An item costs 24 dollars online plus 6 dollars delivery. A local shop charges 29 dollars with no extra fee. Which total is lower?2 marks
- A class has 45 dollars and a planned total of 39 dollars. A possible extra fee is 8 dollars. Would the budget still fit if it is charged?2 marks
- You need eight notebooks. Packs of four cost 6 dollars; packs of ten cost 13 dollars. Compare the lowest cost of each suitable purchase.2 marks
- A stall expects income of 70 dollars and costs of 46 dollars. If income is 10 dollars lower, what surplus remains?2 marks
- Two school bags cost 30 and 35 dollars. No information about durability is given. Can you conclude that the 35-dollar bag will last longer? Explain.2 marks
Read the worked solutions
Equivalent correct methods earn the corresponding marks. Include units where asked.
- A 15-dollar bottle can be used twelve times with free refills. Single-use bottles cost 2 dollars each. How much is saved by choosing the reusable bottle for twelve uses?2 marks
; .
9 dollars. - An item costs 24 dollars online plus 6 dollars delivery. A local shop charges 29 dollars with no extra fee. Which total is lower?2 marks
Online total ; local total 29.
The local shop, by 1 dollar. - A class has 45 dollars and a planned total of 39 dollars. A possible extra fee is 8 dollars. Would the budget still fit if it is charged?2 marks
; .
No; the revised total is 47 dollars, 2 dollars over budget. - You need eight notebooks. Packs of four cost 6 dollars; packs of ten cost 13 dollars. Compare the lowest cost of each suitable purchase.2 marks
; .
Two packs of four cost 12 dollars, which is 1 dollar less than a pack of ten. - A stall expects income of 70 dollars and costs of 46 dollars. If income is 10 dollars lower, what surplus remains?2 marks
Revised income 60; .
14 dollars. - Two school bags cost 30 and 35 dollars. No information about durability is given. Can you conclude that the 35-dollar bag will last longer? Explain.2 marks
More information is needed; it is valid to compare the prices but not invent a lifetime difference.
No. The prices alone do not establish durability.
Curriculum reference & lesson scope
Australian Curriculum v9 and SA Curriculum Mathematics
Fraction/decimal/percentage quantities; discounts; budgets/cost predictions; comparing choices, risks and consequences.
Official curriculum source ↗