Models

Tariffs, tax tables and profit models

Two tariff options: which is cheaper at a given usage. Draw both graphs. Read the better deal.

CAPS

Grade 12 · Mathematical Literacy · Models

Mathematical Literacy uses a context, not a bare sum.

Two papers
Paper 1 uses familiar contexts: pay slips, till slips, maps you have seen, and data in a table. Paper 2 uses less familiar contexts and expects you to decide which method fits. Both papers are 150 marks.
What to show
Write the value with its unit or its rand sign. Say whether you multiply or divide, and round only at the end, in the way the question asked (nearest rand, one decimal place, a whole number of tiles).
The relation
choose the option with the smaller cost at that usage. Compare two deals
How a marker reads it
Show both substitutions. The cheaper option can swap after the break-even usage — find that usage if they ask.

A correct number with the wrong unit, or a VAT amount treated as the full price, loses the mark the context was testing.

Diagram

Worked example

Option A: R50 + R2 per unit. Option B: R0 + R4 per unit. Cheaper at 40 units?

Before any working — hunt first

Given

Numbers and units already in the sentence: R50 · R2 per · R0 · R4 per · 40 units. Copy each one into a column. A name without a number is not given.

Missing

After you copy the given, the letter that still has no number is missing. The paper is pointing at: Cheaper at 40 units. Circle that word — that is the missing variable.

Find

We are required to find: Cheaper at 40 units. Write that as a symbol on the left, with a question mark, before you touch a formula.

Calculate

Write choose the option with the smaller cost at that usage with empty letters. Cross out every letter that already has a number. Calculate the letter that is still standing — that gives Cheaper at 40 units.

Simplified approach

Work out both totals, then compare.

Culture note

Cell C versus Vodacom prepaid vs contract is this comparison, with different numbers.

Formulas

choose the option with the smaller cost at that usage

Compare two deals

Exam tricks you must know

These are the moves markers look for — not shortcuts that skip the method, but the habits that earn the method mark.

Always substitute the usage into both tariff options — the cheaper one can swap after break-even
How:Write cost A and cost B as two lines. Set them equal if they ask where the deals match. Circle the smaller total at the given usage. A graph with two lines makes the swap obvious.
When to use it:Cellphone contracts, prepaid electricity, and cake-sale break-even.
If the price already includes VAT, divide by 1.15 — do not subtract 15%
How:Total = price × 1.15 when VAT is still to be added. When the till already shows VAT, price excluding = total1.15. Subtracting 15% of the total is a different number and loses the mark.
When to use it:Till slips, VAT, and SARS-style tax questions.
Fencing is perimeter. Grass, paint and tiles are area. Tanks are volume.
How:Underline the object: wire, border, fence → add the sides. Floor, wall, field, paint → multiply length by width, then divide by coverage and round tins up. Water in a tank → m³ then × 1 000 for litres.
When to use it:Measurement papers: school fields, paint, Jojo tanks.

Step 1 / 5

Cost A

50+2×40=R130.

A=130B=4×40=160

Why this step: We only do one job per line so a marker can follow the marks — and so you can find a slip without starting over.

4. Step-by-step working

01
Cost A
50+2×40=R130.
A=130B=4×40=160
02
Cost B and compare
B = R160. A is cheaper by R30.

More worked examples

Board walkthroughs on this topic. Open one, copy the working, then try the next.

Example 1 / 20

An item sells for R50 and costs R30 to make. 40 items are sold. Find the profit on one item and the total profit.

4. Step-by-step working

01
Subtract
Profit each=50−30=R20.
R20
02
Multiply
Total profit=20×40=R800.
R800

How we got there

Read this like a teacher at the board. We go slowly, name every number, and say why we take each step.

Explain in another language · 11

1. What is the question asking?

Read the question twice. Circle the unknown. Underline every number and unit. The paper is asking: An item sells for R50 and costs R30 to make. 40 items are sold. Find the profit on one item and the total profit.

In other words — as if you have never seen this before

If you have never seen this before: Profit on one item is selling price minus cost. Total profit multiplies that by how many were sold. Income is not profit. We will name a method in words, write the formula with no numbers, then substitute one line at a time.

2. What do we already know?

Selling price R50, cost R30, number sold 40.

3. Which method — and why this one?

Profit on one item is selling price minus cost. Total profit multiplies that by how many were sold. Income is not profit.

4. Step-by-step working

01 / 05
Subtract
Profit each=50−30=R20.
R20
Why this step: We only do one job per line so a marker can follow the marks — and so you can find a slip without starting over.
02 / 05
Multiply
Total profit=20×40=R800.
R800
Why this step: We only do one job per line so a marker can follow the marks — and so you can find a slip without starting over.
03 / 05
Sense-check
Income would be 50 × 40 = R2000, which still includes the costs.
R800
Why this step: We only do one job per line so a marker can follow the marks — and so you can find a slip without starting over.
04 / 05
Step F — Box the answer with its unit
R20 each. Total profit R800.
Why this step: A number without a unit is half a mark on a Physics paper, and a marker can miss a Maths answer that is buried in working.
05 / 05
Step H — What the marker is looking for
On an NSC memo you usually earn: (1) a method mark for naming the right formula or idea in words, (2) an accuracy mark for substituting the given numbers with units, (3) an accuracy mark for the boxed answer with its unit. Write those three lines even if you are unsure of the arithmetic — blank pages score zero.
Why this step: First-timers chase the final number and leave the method blank. The memo still pays out for the idea and the substitution even when the last line is wrong.

5. The answer

R20 each. Total profit R800.

Copy onto your answer sheet — in this order

Formula: R20

Answer: R20 each. Total profit R800.

6. Check it like a marker

Multiplying the selling price by the number sold is the income. Profit has already subtracted the cost.

7. A trap first-timers fall into

First-timers often grab the first formula they remember, mix units (cm with m, minutes with seconds), or drop a minus sign. Write the formula in words first: “this equals that, because…”

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