Ratio and proportion

Best buy

Compare what your money buys.

Predict, test and explain

Step 1 of 3

Predict

Pack A costs £2.40 for 400 g. Pack B costs £3.20 for 600 g. Which has lower unit price?

unit price=pricemass\text{unit price} = \frac{\text{price}}{\text{mass}}

Price per 100 g100\,\text{g}

Pack A£0.60\text{£}0.60
Pack B≈£0.53\approx \text{£}0.53

Pack B is better value.

2.4400×100=0.60\frac{2.4}{400}\times100 = 0.603.2600×100≈0.53\frac{3.2}{600}\times100 \approx 0.53

InvestigateCan the smaller pack be the better buy?

Explore and compare
Can you break the rule?

The bigger pack is better value.

Always, sometimes or never? Test it in the simulation.

Hint

Compare price per unit. Change the bigger pack’s price while keeping both masses fixed.

Check the reasoning

Sometimes. Pack size alone cannot decide value. The pack with the lower price per unit is better value; equal unit prices mean a tie.

One counterexample disproves “always”. Examples alone do not prove it.

Make the smaller pack better value.

Try it in the simulation. Change one thing at a time.

Hint

Compare each price divided by its mass. The smaller pack needs the lower price per unit.

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Hints, self-check and connections
Try a self-check

Fixed values, separate from the diagram controls.

Four identical pens cost £3. Six cost £4.20. Which pack has the lower price per pen?

Hint

Divide each pack price by its number of pens.

Reveal answer

The six-pack: 70p per pen, compared with 75p per pen in the four-pack.

3÷4=0.75,4.20÷6=0.703\div4=0.75,\qquad4.20\div6=0.70

Build an explanation

Hint 1

Compare equal quantities rather than just the pack prices.

Hint 2

Divide each price by its mass, then multiply by 100 for the price per 100 g.

Hint 3

The smaller unit price gives better value when the products are comparable.

Worked example

This example uses fixed values, separate from the diagram controls.

Pack A costs £2.40 for 400 g; pack B costs £3.20 for 600 g. Which is better value?

  1. A costs £2.40/400 × 100 = £0.60 per 100 g.
  2. B costs £3.20/600 × 100, approximately £0.53 per 100 g.

Answer: Pack B has the lower unit price.

Connect this idea

Watch out: The cheaper pack price does not always mean the better unit price.