Lesson 14 ~25 min Unit 1 · Financial Maths +85 XP

Best Buy, Unit Prices

Cracking the supermarket code: $\$/$100g, $\$/$L, $\$/$unit. Bigger isn't always cheaper.

Today's hook: 500g of pasta costs $\$1.80$. 1kg costs $\$3.20$. Which is the better deal?

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Think First

warm-up

500g of pasta costs $\$1.80$. 1kg costs $\$3.20$. Which is the better deal? Jot down your first reaction, then we'll see who's right.

Record your answer in your workbook.

The Big Idea

+5 XP

To find the best buy, calculate the unit price (cost per fixed amount, per kg, per 100 g, per L). The product with the lowest unit price is cheapest per amount.

500 g pasta for $\$1.80$ means $\$1.80 \div 0.5 = \$3.60$/kg. 1 kg pasta for $\$3.20$ is $\$3.20$/kg. The 1 kg pack is cheaper per kg, $\$0.40$ less! Larger is usually cheaper per unit, but NOT always, always check.

Unit Price $= \dfrac{\text{Total cost}}{\text{Quantity}}$

Same units

Compare $/$kg with $/$kg, not $/$g with $/$kg.

Lower = better

Smaller unit price means cheaper per amount.

Watch the trap

Bigger sizes are USUALLY cheaper per unit, but not always.

What You'll Master

objectives

Know

Unit price = total cost ÷ quantity
Compare in the same units
Lower unit price = cheaper per quantity
Supermarket shelf labels often show unit price

Understand

Why unit prices remove the "package size" confusion
How to spot when a smaller pack is the better deal
Why some “value” packs are not actually value

Can Do

Calculate unit prices for any product
Compare two packages of different sizes
Identify the best buy in a real supermarket scenario

Words You Need

vocabulary

Unit priceCost per fixed unit (e.g., $\$/$kg, $\$/$100 g).

Best buyThe option with the lowest unit price.

Shelf labelOften shows per-unit price below the item price.

Bulk discountWhen buying more reduces the unit price.

Premium pricingWhen smaller packs cost MORE per unit (convenience tax).

ComparisonDirect: same units; indirect: convert first.

Spot the Trap

heads-up

Wrong: "$\$1.80$ for 500g is cheaper than $\$3.20$ for 1kg, because $\$1.80 < \$3.20$", NO. You're comparing totals, not unit prices.

Right: Compare unit prices: $\$3.60/$kg vs $\$3.20/$kg. The 1 kg is cheaper PER kg.

Wrong: "Bigger packs are ALWAYS cheaper per unit.", Not true. Sometimes smaller packs are on sale.

Right: Always calculate. The 500 g pack might be on sale and beat the 1 kg.

Unit Price Calculation

+5 XP

Divide the total cost by the amount. Pick a sensible “1 unit”: per 100 g, per kg, per L.

A 600 g jar of jam costs $\$5.40$. Per 100 g: $5.40 \div 6 = \$0.90$ per 100 g. Or per kg: $5.40 \div 0.6 = \$9.00$/kg. Both correct, choose the unit that makes comparison easiest.

Unit Price $= \dfrac{\text{Cost}}{\text{Quantity in chosen unit}}$

Pick a sensible unit

$/$kg, $/$L, $/$100 g, $/$mL.

Per 100 g for small items

Avoids tiny decimal values.

Per kg or per L for big

Easier to compare bulk.

Comparing Different Products

+5 XP

Convert all options to the SAME unit. Then the lowest unit price wins.

Brand A: 250 g cereal for $\$3.50$ $\to \$14$/kg. Brand B: 500 g for $\$6$ $\to \$12$/kg. Brand C: 1 kg for $\$13.50$ $\to \$13.50$/kg. Best buy: Brand B at $\$12$/kg. Beware Brand C, bigger but not cheaper.

Best buy $=$ MIN(unit prices)

Convert all

To the same unit first.

Compare

Smallest unit price wins.

Trust the maths

Not the package size!

Watch Me Solve It · 3 examples

Watch Me Solve It · The pasta

+15 XP per step

PROBLEM

500 g pasta for $\$1.80$ vs 1 kg pasta for $\$3.20$. Which is the better buy?

1

Unit price of 500 g pack

$\$1.80 \div 0.5 = \$3.60$/kg

Per kg.
2

Unit price of 1 kg pack

$\$3.20 \div 1 = \$3.20$/kg

Per kg.
3

Compare

$\$3.20 < \$3.60$

1 kg is cheaper per kg, better buy.

Answer1 kg pack, $\$0.40/$kg cheaper

Watch Me Solve It · Cereal showdown

+15 XP per step

PROBLEM

250 g box for $\$4.00$ vs 400 g box for $\$5.60$. Which is cheaper per 100 g?

1

Per 100 g for 250 g pack

$\$4.00 \div 2.5 = \$1.60/$100 g

Divide by 2.5.
2

Per 100 g for 400 g pack

$\$5.60 \div 4 = \$1.40/$100 g

Divide by 4.
3

Compare

$\$1.40 < \$1.60$

400 g is cheaper per 100 g.

Answer400 g pack at $\$1.40/$100 g

Watch Me Solve It · Watch for the trap

+15 XP per step

PROBLEM

2 L bottle of cordial for $\$5.00$ vs $1.5$ L for $\$3.60$. Which is cheaper per L?

1

2 L bottle

$\$5.00 \div 2 = \$2.50$/L

Per litre.
2

1.5 L bottle

$\$3.60 \div 1.5 = \$2.40$/L

Per litre.
3

Compare

$\$2.40 < \$2.50$

1.5 L is cheaper per L, the BIGGER bottle is NOT better here.

Answer1.5 L bottle at $\$2.40$/L

Common Pitfalls

heads-up

Comparing totals not unit prices

Picking the cheaper-LOOKING package without per-unit maths.

Fix: Always calculate per kg, per L, per 100 g.

Mixed units

Comparing $\$/$100 g with $\$/$kg.

Fix: Convert one or the other so both are in the same unit.

Assuming bigger is cheaper

Sometimes the medium size is on special.

Fix: Calculate every time. Trust the numbers.

Copy Into Your Books

Formula

Unit price = cost ÷ quantity
Pick sensible unit
Per kg, per L, per 100 g

Sensible Units

Solids: per kg or per 100 g
Liquids: per L or per 100 mL
Loose items: per kg

Compare

Same units for all options
Lower unit price = better buy
Convert if needed

Watch For

"Family size" can be more expensive per unit
Sales can flip the usual order
Always verify with maths

How are you completing this lesson?

Brain Trainer · 4 problems

Brain Trainer · Best Buy, Unit Prices

4 problems

Four drill problems to sharpen your skills. Work each, then reveal the answer.

1 $\$6$ for 750 g cheese. Per kg?

$\$6 \div 0.75 = \$8/$kg.$\$8/$kg
2 Compare $\$3.20$/L vs $\$1.50/$500 mL.

$1.50/0.5 = \$3/$L < \$3.20/$L. 500 mL is better.$\$3.00/$L is best
3 1.2 kg rice for $\$4.80$. Per 100 g?

$\$4.80 \div 12 = \$0.40/$100 g.$\$0.40/$100 g
4 Brand A $\$2.10/$500 g vs Brand B $\$3.50/$kg.

A: $\$2.10/0.5 = \$4.20/$kg. B: $\$3.50/$kg. B wins.Brand B

Complete in your workbook.

Quick Check · 5 questions

A 400 g pack of chips costs $\$4. Per 100 g, this is:

+10 XP

Which is the better buy? Pack A: 500 g for $\$4$; Pack B: 1 kg for $\$7.50$.

+10 XP

2 L of juice for $\$6.40$ vs $1.5$ L for $\$5.10$. Better buy:

+10 XP

500 g of bananas at $\$2.50$. Per kg:

+10 XP

Mia compares two laundry powders: $\$15$ for 2 kg, $\$22$ for 3 kg. Cheaper per kg:

+10 XP

Show Your Working · 3 questions

Show Your Working

9 marks total

Apply Medium 3 MARKS

Q6. Calculate the unit price for each (use the unit shown): (a) 750 g of rice for $\$3.75$ (per kg); (b) 200 mL of cordial concentrate for $\$4.00$ (per 100 mL); (c) 12 eggs for $\$5.40$ (per egg).

Answer in your workbook.

Understand Easy 2 MARKS

Q7. A 1.5 kg bag of dog biscuits costs $\$12.60$ and a 4 kg bag costs $\$32$. Which is cheaper per kg, and by how much?

Answer in your workbook.

Reason Hard 4 MARKS

Q8. A supermarket sells the same olive oil three ways: $250$ mL at $\$5$, $500$ mL at $\$8.50$, $1$ L at $\$15.50$. (a) Find the unit price (per $100$ mL) for each. (b) Rank cheapest to most expensive per 100 mL. (c) The shopper only needs $400$ mL. What is the cheapest way to buy at least $400$ mL?

Answer in your workbook.

Comprehensive Answers

Quick Check

1. B$\$1.00$/100 g.

2. A Pack B at $\$7.50/$kg vs Pack A at $\$8/$kg.

3. A2 L at $\$3.20/$L.

4. D$\$5.00/$kg.

5. B3 kg pack.

Show Your Working Model Answers

Q6 (3 marks): (a) $3.75 \div 0.75 = \$5/$kg [1]. (b) $4 \div 2 = \$2.00/$100 mL [1]. (c) $5.40 \div 12 = \$0.45/$egg [1].

Q7 (2 marks): $1.5$ kg: $\$12.60/1.5 = \$8.40$/kg [1]. $4$ kg: $\$32/4 = \$8.00$/kg. $4$ kg is $\$0.40$/kg cheaper [1].

Q8 (4 marks): (a) $250$ mL: $5/2.5 = \$2.00/$100 mL. $500$ mL: $8.50/5 = \$1.70/$100 mL. $1$ L: $15.50/10 = \$1.55/$100 mL [2]. (b) $1$ L $<$ $500$ mL $<$ $250$ mL (cheapest to dearest per 100 mL) [1]. (c) For at least 400 mL: one $500$ mL bottle at $\$8.50$ beats two $250$ mL ($\$10$) and is cheaper than the $1$ L ($\$15.50$). Best: $500$ mL for $\$8.50$ [1].

Stretch Challenge · +25 XP, +10 coins

The Cleverer Cheaper

A supermarket sells the same chocolate bar in two ways: a 100 g bar for $\$2.50$, or a 4-pack of $100$ g bars for $\$9$. The 4-pack is on sale: “Buy one, get one $50\%$ off”. (a) What is the unit price for the single bar? (b) What is the unit price for the 4-pack at the sale price? (c) What is the cheapest way to buy 8 bars worth of chocolate?

Reveal solution

(a) Single: $\$2.50/$100 g $= \$2.50/$bar. (b) Sale: 1 pack at $\$9$ + 1 pack at $50\%$ off ($\$4.50$) = $\$13.50$ for 8 bars = $\$1.6875/$bar. (c) Buying two 4-packs (one full, one half-price) gives 8 bars for $\$13.50$, cheapest. Buying 8 singles costs $\$20$, much worse.

Quick Review

Unit price

Cost ÷ quantity

Pick a unit

$/$kg, $/$L, $/$100 g

Same unit

Convert to compare

Lower = better

Smaller unit price wins

Calculate always

Don't guess from size

Sales flip things

Always check the maths

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