The idea, step by step
Compare what the choice really provides
A low price per item can still require more money than you have. Check the total cost, the quantity needed and whether unused items will be useful later. State the question being answered: cheapest per item and cheapest suitable purchase are not always the same.
Other factors may matter, such as durability, waste, delivery and the time an item will be used. Do not invent a numerical value for these factors if none is supplied; explain the trade-off honestly.
Test a possible extra cost
A financial risk is something uncertain that could affect the plan. Ask what changes if a fee is added, an item breaks or fewer goods are sold. Use a simple alternative calculation with supplied amounts.
Choose only after checking the assumptions. A conclusion can be reasonable without being the only possible choice, provided the calculations are correct and the reason fits the stated needs and budget.
A common trap
The cheapest-looking option is always best, even if its final total exceeds the budget.
Instead: Check the complete amount to pay and the required quantity. Then consider relevant non-price consequences.
See the thinking
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.
- Ten disposable bottles cost 10×2=20 dollars.
- The reusable bottle costs 12 dollars for the same ten uses, so it costs 8 dollars less.
- The conclusion assumes the reusable bottle lasts for all ten uses and no refill fee applies.
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 |
- Museum total: 12+18+6=36 dollars.
- Park total including shelter: 0+15+6+5=26 dollars.
- The park remains 10 dollars cheaper, though weather and activities may also affect the choice.
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
The pack of ten.
It meets the need and fits the budget. The larger pack is cheaper per pen but costs more than the available 6 dollars.
Your turn
6 questions · 12 marks · Work at your own pace.
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
12×2=24; 24−15=9.
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 24+6=30; 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
39+8=47; 47−45=2.
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
2×6=12; 13−12=1.
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; 60−46=14.
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 ↗