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