Direct Proportion and Value for Money
Direct proportion and value for money covers comparing the prices of differently sized packs by working out a unit price, such as the price per single item or per 100 g, to decide which one gives more for the money. This applies direct proportion to a consumer-maths context that appears regularly on 11+ papers, and it tests whether a pupil can put two options on a fair, equal footing before comparing them.
Method
- Identify the options being compared and the total price and quantity of each.
- Find the unit price of each option by dividing its total price by its quantity, or by dividing the quantity by the price, depending on which is easier.
- Make sure every option's unit price uses the same unit of measurement, for example pence per gram for every pack, not grams for one and kilograms for another.
- Compare the unit prices directly: the smaller price per unit is the better value for money.
- Where the question asks how much cheaper one option is overall, use the unit prices to work out the cost of an equal quantity from each option, then subtract.
- State the final answer clearly, naming which option is better value and giving a reason based on the unit price.
Worked example
A 400 g box of cereal costs 2.40 pounds. A 600 g box of the same cereal costs 3.30 pounds. Which box offers better value for money?
- Find the price per 100 g for the small box: 2.40 / 400 x 100 = 0.60 pounds per 100 g.
- Find the price per 100 g for the large box: 3.30 / 600 x 100 = 0.55 pounds per 100 g.
- Compare the two unit prices: 0.55 pounds per 100 g is less than 0.60 pounds per 100 g.
- Final answer: the 600 g box is better value, since it costs less per 100 g.
Practice questions
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Q1A 5-pack of pens costs 2 pounds. Find the price per pen.Show answer
Answer: 0.40 pounds (2 / 5)
Q2A 250 g jar of jam costs 1.50 pounds. Find the price per 100 g.Show answer
Answer: 0.60 pounds (1.50 / 250 x 100)
Q3Which is better value: 3 apples for 90p, or 5 apples for 1.40 pounds?Show answer
Answer: 5 apples for 1.40 pounds (28p per apple, compared with 30p per apple)
Q4A 12-pack of juice cartons costs 4.80 pounds. Find the price per carton.Show answer
Answer: 0.40 pounds (4.80 / 12)
Q5A 2-litre bottle of squash costs 3.00 pounds and a 3-litre bottle costs 4.20 pounds. Which is better value per litre?Show answer
Answer: The 3-litre bottle (1.40 pounds per litre, compared with 1.50 pounds per litre)
Q6True or False: the pack with the lowest total price is always the best value for money.Show answer
Answer: False (a smaller pack often costs less in total even though it costs more per item or per gram)
Q7Explain why comparing the total prices of two differently sized packs, without finding a unit price, can be misleading.Show answer
Answer: A larger pack usually costs more in total even if it is the cheaper option per item or per gram, so comparing totals alone does not show which pack gives more product for each pound spent; finding the unit price puts both packs on a fair, equal footing.
Exam-style questions
Written in the style of a 11+ exam paper, with a full mark scheme.
A 750 ml bottle of shampoo costs 4.50 pounds. A 500 ml bottle of the same shampoo costs 3.20 pounds. Work out the price per 100 ml for each bottle, and state which is better value.
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A supermarket sells rice in three sizes: a 500 g bag for 1.00 pound, a 1 kg bag for 1.80 pounds, and a 2.5 kg bag for 4.00 pounds. (a) Work out the price per 100 g for each bag. (b) State which bag is the best value for money. (c) Work out how much would be saved by buying five of the 500 g bags instead of one 2.5 kg bag, for the same total quantity of rice.
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Free printable worksheet
Want more practice on paper? Download the direct proportion and value for money worksheet pack - 8 pages of exam-style questions with a full mark scheme. One email opens every download in this browser for 14 days - no account, no card. Print it for personal and classroom use.
This topic is chapter 8 of 11+ Maths Workbook 2, the whole course as one free printable PDF.
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