EST. 2024 · LONDON·MMXXVI SPECIFICATION
AQA·Edexcel·OCR|Foundation + Higher
Ratio, Proportion & Rates of Change

Sheet № 226 · Foundation + Higher · AQA · Edexcel · OCR

226

Recipe and Scaling Problems –

Recipe and scaling problems are among the most common ratio questions on GCSE Maths papers. They test your ability to increase or decrease quantities proportionally — a skill used daily in cooking, manufacturing and science. These questions give you a recipe for a certain number of servings and ask you to adjust the ingredients for a diff

§Key definitions

Question:

A recipe for 8 pancakes uses 200 g flour, 2 eggs and 300 ml milk. How much of each ingredient is needed for 20 pancakes?

Answer:

500 g flour, 5 eggs, 750 ml milk.

Q1 (Foundation):

A cake recipe for 12 cupcakes uses 180 g sugar. How much sugar is needed for 18 cupcakes?

Q2 (Foundation):

A recipe for 5 portions uses 400 g pasta. How much pasta is needed for 3 portions?

Q3 (Higher):

A recipe for 4 servings uses 300 g rice, 200 g chicken and 150 ml sauce. Tom wants to make 10 servings but only has 700 g of rice. Can he make 10 servings? If not, what is the maximum number of whole servings he can make?

§Formulas to memorise

Scale factor = New number of servings / Original number of servings

New amount = Original amount x Scale factor

Amount for 1 serving = Original amount / Original servings

Write down what you know: — the original recipe (servings and ingredient amounts) and the target number of servings.

Find the scale factor — by dividing the target servings by the original servings.

Multiply every ingredient — by the scale factor.

Check — that all ingredients have been scaled and that the answer is sensible.

Worked example

A recipe for 8 pancakes uses 200 g flour, 2 eggs and 300 ml milk. How much of each ingredient is needed for 20 pancakes?

Working:

Common mistakes

  • Only scaling one ingredient. You must multiply every ingredient by the same scale factor to keep the recipe in proportion.
  • Getting the scale factor upside down. The scale factor is new amount divided by original, not the other way round. A scale factor less than 1 means you are scaling down.
  • Forgetting to convert units. If the question gives one ingredient in kilograms and another in grams, convert to the same unit before comparing.
  • Giving a fractional answer for items that must be whole. You cannot use 2.5 eggs in practice — but in a GCSE exam, give the exact mathematical answer unless told otherwise.

Exam tips

  • Always show the scale factor calculation — it earns a method mark even if you make an error later.
  • If a question asks for the "maximum number of servings" from a limited ingredient, divide the available amount by the per-serving amount and round down.
  • The unitary method works well when the scale factor is not a whole number or is difficult to spot.
  • Read the question carefully to see whether you are scaling up or scaling down.
MMXXVI specification · AQA · Edexcel · OCRgcsemathsai.co.uk/formulas/recipe-and-scaling-problems