Understand the idea.
Represent the important costs
Separate a fixed cost from a cost charged for each person or item. Pay the fixed amount once; multiply the per-person amount by the group size. For transport costing dollars plus entry per student, the total for students is dollars.
To find an affordable group size, reserve the fixed cost first and use the remaining budget for entries. Students must be counted in whole numbers. Check the proposed maximum and the next larger group, rather than reporting only a division result.
| Students | Transport in dollars | Entry in dollars | Total in dollars |
|---|---|---|---|
| 5 | 30 | 30 | 60 |
| 10 | 30 | 60 | 90 |
| 15 | 30 | 90 | 120 |
Check the model against the situation
A model keeps the important quantities and states its assumptions. The trip calculation assumes unchanged entry prices, enough transport seats and no other compulsory fees. A correct calculation predicts the real cost only while those assumptions remain suitable.
For a fundraiser, distinguish income from costs: money left is income minus all required spending. Check a model against a small case or a new quote, and revise it when an additional fee, discount or capacity limit changes the situation.
See the method in action.
Find an affordable group size
Transport costs 30 dollars and entry costs 6 dollars per student. The budget is 150 dollars. Assuming transport has enough seats, what is the largest affordable number of students?
Worked solution
- 1
Reserve the fixed transport cost.
Transport is paid once, leaving this amount for student entries.
- 2
Find the number of entries available.
Each student requires six dollars of the remaining budget.
- 3
Check the proposed maximum.
Twenty students use exactly the budget, assuming enough seats.
- 4
Test one additional student.
The next whole group size exceeds the budget; further students only increase the cost.
20 students
Find the fundraiser surplus
A stall sells 30 items for 2.50 dollars each. Materials cost 1.50 dollars per item and setup costs 20 dollars once. Find the money left after costs.
Worked solution
- 1
Calculate the sales income.
Each of the thirty sold items brings in two dollars fifty.
- 2
Calculate the material spending.
The material cost applies to each item, not just once.
- 3
Include the fixed setup cost.
The setup fee is added once to the total material cost.
- 4
Subtract all costs from income.
The surplus is the money remaining after both types of cost are paid.
10 dollars
Try it yourself.
Check your understanding
A venue charges 10 dollars once plus 4 dollars per person. Find the total for 6 people.
Show answer & reasoning
34 dollars
Six people cost dollars in per-person charges. Add the one-off fee once: dollars.
Keep practising
6 worksheet questions · 17 marks
Read the questions online
- An excursion has a 20-dollar booking fee and costs 5 dollars per person. Find the cost for 8 people.2 marks
- A game venue costs 10 dollars once plus 4 dollars per person. Find the total for 0, 1 and 2 people.2 marks
- A stall sells 10 items for 3 dollars each. Materials cost 1 dollar per item, plus a 15-dollar setup fee. Find the surplus.3 marks
- A ticket model uses 7 dollars per person. Give two things that should be checked before using it to predict the cost of a school trip.3 marks
- Company A charges 40 dollars once plus 2 dollars per person. Company B charges 6 dollars per person with no fixed fee. Both can carry 12 people. Which is cheaper for 12 people?3 marks
- You have 80 dollars for kits. Delivery costs 18 dollars once and each kit costs 7.50 dollars. Find the largest number of whole kits you can buy and the money left.4 marks
Read the worked solutions
Equivalent correct methods earn the corresponding marks. Include units where asked.
- An excursion has a 20-dollar booking fee and costs 5 dollars per person. Find the cost for 8 people.2 marks
dollars.
60 dollars - A game venue costs 10 dollars once plus 4 dollars per person. Find the total for 0, 1 and 2 people.2 marks
The fixed fee remains 10 dollars. Add 0, 4 or 8 dollars.
10, 14 and 18 dollars. - A stall sells 10 items for 3 dollars each. Materials cost 1 dollar per item, plus a 15-dollar setup fee. Find the surplus.3 marks
dollars. dollars.
dollars.
5 dollars - A ticket model uses 7 dollars per person. Give two things that should be checked before using it to predict the cost of a school trip.3 marks
The model needs an appropriate per-person price and all fixed fees. Other reasonable cost or capacity assumptions are acceptable.
For example: whether all students pay 7 dollars; whether a booking or transport fee must be added. - Company A charges 40 dollars once plus 2 dollars per person. Company B charges 6 dollars per person with no fixed fee. Both can carry 12 people. Which is cheaper for 12 people?3 marks
A costs dollars.
B costs dollars.
A is cheaper by 8 dollars. - You have 80 dollars for kits. Delivery costs 18 dollars once and each kit costs 7.50 dollars. Find the largest number of whole kits you can buy and the money left.4 marks
After delivery, 62 dollars remains. Eight kits cost 60 dollars; nine cost 67.50 dollars.
dollars; dollars.
8 kits; 2 dollars left.
Curriculum reference & lesson scope
Australian Curriculum v9 / SA Curriculum Mathematics
Fractions–decimals–percentages; percentages of quantities; expressing one amount as a percentage of another; discounts and sale prices; practical spending/budget comparisons; choosing and explaining a financial model.
Official curriculum source ↗