Year 7 Maths • AC9M7M06 • Homework
Mathematical Modelling with Ratios
Formulate ratio models, connect part–part and part–whole representations, solve practical problems, and communicate what your answer means in context. Show working and include units.
Part A • 10 marks
Short-response questions
The ratio sugar:other ingredients is 3:7. Write sugar as a fraction of the whole mixture. (2 marks)
Simplify the ratio 12:18. (2 marks)
A drink uses syrup:water = 1:4. What fraction of the drink is syrup? (2 marks)
A dye mix uses red:yellow = 2:3. Which colour is the greater proportion, and how do you know? (2 marks)
Write 250 mL oil : 50 mL vinegar as a ratio in simplest form. (2 marks)
Part B • 25 marks
Extended-response questions
A concrete mix uses cement:sand:gravel = 1:2:3. If the total mass is 48 kg, calculate the mass of each ingredient. Show working and check that your amounts total 48 kg. (5 marks)
A salad dressing uses oil:vinegar = 3:1. If vinegar is 40 mL, find the amount of oil and the total volume. Explain how the ratio is preserved. (5 marks)
A textile dye uses blue:red = 5:2. If the total dye is 210 mL, find the amount of each colour. (5 marks)
A colour model uses red:blue = 4:1. Describe how counters or a bar model could represent the ratio, then determine the fraction of the model that is red. (5 marks)
A verified commercial formulation uses ingredient A:carrier = 3:2. If the carrier amount is 50 mL, determine ingredient A. Then explain why a mathematical model must still be interpreted with the real-world instructions, units and constraints of the formulation. (5 marks)
Part C • Enrichment
Scale, represent and justify
11. A verified product formulation is modelled using ingredient A : binder : carrier = 4:1:5. You need 300 mL in total. Calculate the amount of each component. Represent the ratio using either a bar model, table or equation, and justify why your chosen representation is useful. Finally, explain one practical constraint that should be checked before using the mathematical result.
Teacher / checking section
Answers
1. Part-whole fraction
Total parts = 3 + 7 = 10, so sugar is 3/10 of the whole.
2. Simplify 12:18
Divide both terms by 6: 2:3.
3. Syrup fraction
Total parts = 5, so syrup is 1/5.
4. Greater proportion
Yellow, because the ratio has 3 yellow parts for every 2 red parts.
5. Oil:vinegar
250:50 = 5:1.
6. Concrete
Total parts = 6; one part = 48 ÷ 6 = 8 kg. Cement = 8 kg, sand = 16 kg, gravel = 24 kg. Check: 8 + 16 + 24 = 48 kg.
7. Dressing
Vinegar is one part = 40 mL. Oil = 3 × 40 = 120 mL. Total = 160 mL.
8. Textile dye
Total parts = 7; one part = 210 ÷ 7 = 30 mL. Blue = 150 mL; red = 60 mL.
9. Representation
For example, use 4 red counters and 1 blue counter or a five-block bar. Red is 4/5 of the whole model.
10. Formulation modelling
Carrier = 2 parts = 50 mL, so one part = 25 mL and ingredient A = 75 mL. A sound response also notes that units, instructions, measurement precision and other real-world constraints must be respected.
11. Enrichment
Total parts = 10; one part = 30 mL. Ingredient A = 120 mL, binder = 30 mL, carrier = 150 mL. Accept a correct bar model, ratio table or equation such as 4x + x + 5x = 300. A valid practical constraint could include measurement precision, packaging increments, verified instructions, safety requirements or another context-specific condition.