Budgeting and financial assumptions | Year 9

01 / LEARN

Understand the idea.

Account for the whole plan

A budget compares expected income with every planned use of money. Add costs and any reserve once each, then subtract the total from income. A positive balance is money available; a negative balance identifies a shortfall.

For a stall, distinguish a fixed expense from a cost per item. Income depends on items actually sold under the stated assumption. A reserve is money set aside, so exclude it from what can be spent elsewhere.

Check an uncertain assumption

Budgets depend on assumptions about sales, prices and costs. Recalculate with fewer sales or a higher expense to see how the balance changes. Keep fixed costs unchanged unless the new scenario explicitly changes them.

Use one currency and label totals clearly. A reserve can cover unexpected costs, but only if it has already been allowed for. Explain the balance under the supplied assumptions rather than treating projected income as guaranteed.

02 / WORKED EXAMPLES

See the method in action.

EXAMPLE 01

Worked example

A class has 240 dollars. Transport costs 135 dollars, materials 58 dollars and a reserve 20 dollars. Find the balance.

Worked solution

1
Add every planned use of the funds.
$135 + 58 + 20 = 213 dollars$
Transport, materials and the reserve all reduce the amount available to spend.
2
Subtract from the available funds.
$240 - 213 = 27 dollars$
The balance is income or available money minus the planned total.
3
Interpret the positive balance.
$27 > 0$
AUD 27.00 remains available after preserving the separate 20-dollar reserve.

Answer

AUD 27.00 remains

EXAMPLE 02

Worked example

A stall sells 30 items at 6 dollars each. Fixed costs are 50 dollars and each item costs 2 dollars to make. Find the surplus.

Worked solution

1
Calculate the income from sales.
$30 \times 6 = 180 dollars$
Each of the 30 sold items earns 6 dollars.
2
Find the variable production cost.
$30 \times 2 = 60 dollars$
Making each of the 30 items costs 2 dollars.
3
Include the fixed cost once.
$50 + 60 = 110 dollars$
The 50-dollar fixed expense does not multiply by the item count.
4
Find and interpret the surplus.
$180 - 110 = 70 dollars$
Sales exceed the stated costs by AUD 70.00 under the assumed sales count.

Answer

AUD 70.00

03 / YOUR TURN

Try it yourself.

Check your understanding

Income is 90 dollars and costs are 105 dollars. What is the balance?

Show answer & reasoning

AUD 15.00 shortfall

The balance is $90 - 105 = - 15$ dollars. The negative sign means costs exceed income, so this is an AUD 15.00 shortfall rather than money remaining.

Keep practising

6 worksheet questions · 15 marks

Open worksheet Worked solutions

Read the questions online

A budget has 300 dollars income and costs of 125, 84 and 36 dollars. Find the balance.
2 marks
A budget has 300 dollars income, costs of 125, 84 and 36 dollars, and a 20-dollar reserve. Find the remaining available balance.
2 marks
A stall sells 20 items at 5 dollars. Costs are 30 dollars plus 2 dollars per item. Find its surplus.
3 marks
A stall sells and makes 15 items at 5 dollars each. Costs are 30 dollars fixed plus 2 dollars per item. Find the surplus.
3 marks
A 160-dollar transport estimate rises by 10%. How much extra must the budget allow?
2 marks
A plan balances only if every one of 40 tickets sells. Give a useful numerical stress test.
3 marks

Read the worked solutions

Equivalent correct methods earn the corresponding marks. Include units where asked.

A budget has 300 dollars income and costs of 125, 84 and 36 dollars. Find the balance.
2 marks
Costs $= 125 + 84 + 36 = 245$ .
$300 - 245 = 55$ .
AUD 55.00 remains
A budget has 300 dollars income, costs of 125, 84 and 36 dollars, and a 20-dollar reserve. Find the remaining available balance.
2 marks
$55 - 20 = 35$ .
AUD 35.00
A stall sells 20 items at 5 dollars. Costs are 30 dollars plus 2 dollars per item. Find its surplus.
3 marks
Income $= 100$ ; costs $= 30 + 40 = 70$ .
$100 - 70 = 30$ .
AUD 30.00
A stall sells and makes 15 items at 5 dollars each. Costs are 30 dollars fixed plus 2 dollars per item. Find the surplus.
3 marks
Income $= 75$ ; costs $= 30 + 30 = 60$ .
Surplus $= 15$ .
AUD 15.00
A 160-dollar transport estimate rises by 10%. How much extra must the budget allow?
2 marks
$0.10 \times 160 = 16$ .
AUD 16.00
A plan balances only if every one of 40 tickets sells. Give a useful numerical stress test.
3 marks
Keep all fixed costs unchanged.
Use $30 p$ rather than $40 p$ for ticket price $p$ , then check for a shortfall.
Recalculate income and balance for fewer sales, for example 30 tickets.

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Curriculum reference & lesson scope

Australian Curriculum v9 / SA Curriculum Mathematics

Year 9 financial modelling within AC9M9A05 and AC9M9M05; supplied hypothetical rates and costs, not financial advice.

Official curriculum source ↗

In this lesson

Understand the idea.

Account for the whole plan

Check an uncertain assumption

See the method in action.

Worked example

Add every planned use of the funds.

Subtract from the available funds.

Interpret the positive balance.

Worked example

Calculate the income from sales.

Find the variable production cost.

Include the fixed cost once.

Find and interpret the surplus.

Try it yourself.

Check your understanding

Keep practising