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 different number. The key is finding a scale factor or using the unitary method. This guide covers both approaches with clear worked examples for Foundation and Higher tier.

What Are Recipe and Scaling Problems?

A recipe problem gives you a list of ingredient amounts for a certain number of servings. You then need to work out the amounts for a different number of servings, keeping all ingredients in the same ratio.

Key Formulas

Alternatively, using the unitary method: find the amount for one serving first, then multiply by the number you need.

Step-by-Step Method

1. Write down what you know: the original recipe (servings and ingredient amounts) and the target number of servings.
2. Find the scale factor by dividing the target servings by the original servings.
3. Multiply every ingredient by the scale factor.
4. Check that all ingredients have been scaled and that the answer is sensible.

Using the unitary method (alternative)

1. Divide each ingredient by the original number of servings to find the amount for one serving.
2. Multiply each "one serving" amount by the target number of servings.

Worked Example 1 — Foundation Level

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?

Working:

Scale factor = 20 / 8 = 2.5

• Flour: 200 x 2.5 = 500 g
• Eggs: 2 x 2.5 = 5 eggs
• Milk: 300 x 2.5 = 750 ml

Answer: 500 g flour, 5 eggs, 750 ml milk.

Worked Example 2 — Higher Level

Question: A recipe for 6 people uses 450 g of chicken. Raj has 1.2 kg of chicken. What is the maximum number of whole servings he can make?

Working:

Step 1: Convert to the same unit. 1.2 kg = 1200 g.

Step 2: Chicken per serving = 450 / 6 = 75 g.

Step 3: Number of servings = 1200 / 75 = 16 servings.

Answer: Raj can make 16 servings.

Worked Example 3 — Exam Style

Question: A smoothie recipe for 4 glasses uses 240 g strawberries, 160 ml yoghurt and 200 ml apple juice. Beth wants to make 6 glasses but only has 300 g of strawberries. Does she have enough strawberries?

Working:

Scale factor for 6 glasses = 6 / 4 = 1.5

Strawberries needed = 240 x 1.5 = 360 g

Beth only has 300 g, which is less than 360 g.

Answer: No, Beth does not have enough strawberries. She needs 360 g but only has 300 g.

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.

Practice Questions

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?

Practise recipe and scaling problems with personalised feedback free on GCSEMathsAI.

Related Topics

• Ratio Basics and Sharing
• Ratio Problem Solving in Context
• Direct and Inverse Proportion

Summary

• Recipe problems require you to scale all ingredients by the same factor to keep them in proportion.
• The scale factor = new servings / original servings.
• The unitary method finds the amount per one serving first, then multiplies by the required number.
• Always convert to the same units before calculating.
• For "maximum servings" questions, divide the available amount by the per-serving requirement and round down.
• Show your scale factor or unitary calculation to earn method marks.