291","revisionId":"b69fdebe-6e1b-4a18-8f46-ed39afa8f12d","questionNumber":null,"questionType":"LA","specification":"","difficulty":3,"difficultyBand":"medium","totalMarks":4,"sourceTitle":null,"calculatorUse":"non_calc","parts":[{"id":"01c91ade-406e-48fd-b3b7-0485920f6b87","label":"a","content":"Sarah is going to make some fruit punch.\nShe needs to mix apple juice, orange juice and pineapple juice in the ratio $3 : 4 : 2$\n\nSarah wants to make $1800$ ml of fruit punch.\n\nSarah has:\n$500$ ml of apple juice\n$900$ ml of orange juice\n$450$ ml of pineapple juice\n\nDoes Sarah have enough apple juice, orange juice and pineapple juice to make the fruit punch?\nYou must show all your working.","markscheme":"- Calculate value of one part: $1800 \\div 9 = 200$ M1\n- Calculate required amounts: Apple = $3 \\times 200 = 600$, Orange = $4 \\times 200 = 800$, Pineapple = $2 \\times 200 = 400$ M1\n- Compare required with available: $500 < 600$, $900 > 800$, $450 > 400$ M1\n- Conclusion: No, she does not have enough (apple juice). A1","marks":4,"order":0,"markingRubric":{"totalMarks":4,"points":[{"id":"p1","marks":1,"description":"Evidence of dividing total volume by the sum of ratio parts ($1800 \\div 9$).","code":"M"},{"id":"p2","marks":1,"description":"Calculates the required amounts for all three juices: $600, 800, 400$.","code":"M"},{"id":"p3","marks":1,"description":"Compares calculated requirements with the amounts Sarah has available.","code":"M"},{"id":"p4","marks":1,"description":"Correct conclusion (No) based on working, identifying that apple juice is insufficient.","code":"A"}],"finalAnswers":["No","Sarah does not have enough"],"generatedAt":"2026-05-06T14:05:22.515Z","modelVersion":"gemini-3-flash-preview"},"explanation":{"methods":[{"id":"unitary_ratio","label":"Find one ratio part","steps":[{"type":"text","order":0,"title":"Add the ratio parts","content":"The ratio has $3+4+2=9$ equal parts altogether. Divide the total volume by this number to find the volume represented by one part.","highlights":[{"text":"ratio $3 : 4 : 2$","location":"specification"},{"text":"$$1800$ ml of fruit punch","location":"specification"}]},{"type":"text","order":1,"title":"Find one part","content":"Divide the total volume by the $9$ ratio parts:\n\n$$1800\\text{ ml}\\div 9=200\\text{ ml}$$\n\nThis earns the first M1 mark."},{"type":"hyper_latex","block":{"nodes":[{"latex":"$$\\text{Apple}=\\htmlData{anchor=appleparts}{3}\\times\\htmlData{anchor=appleunit}{200}=\\htmlData{anchor=applerequired}{600\\text{ ml}}$"},{"latex":"$$\\text{Orange}=\\htmlData{anchor=orangeparts}{4}\\times\\htmlData{anchor=orangeunit}{200}=\\htmlData{anchor=orangerequired}{800\\text{ ml}}$"},{"latex":"$$\\text{Pineapple}=\\htmlData{anchor=pineparts}{2}\\times\\htmlData{anchor=pineunit}{200}=\\htmlData{anchor=pinerequired}{400\\text{ ml}}$"}],"highlights":[{"color":"red","style":"text-color-with-background","anchor":"applerequired"},{"color":"orange","style":"text-color-with-background","anchor":"orangerequired"},{"color":"amber","style":"text-color-with-background","anchor":"pinerequired"}]},"order":2,"title":"Calculate each amount","description":"Multiply one part by each juice's ratio number. Correctly calculating the required amounts earns the second M1 mark."},{"type":"text","order":3,"title":"Compare every juice","content":"Compare what Sarah **has** with what she **needs**:\n\n- Apple: $500<600$, so there is not enough.\n- Orange: $900>800$, so there is enough.\n- Pineapple: $450>400$, so there is enough.\n\nShowing all three comparisons earns the third M1 mark.","highlights":[{"text":"$$500$ ml of apple juice","location":"specification"},{"text":"$$900$ ml of orange juice","location":"specification"},{"text":"$$450$ ml of pineapple juice","location":"specification"}]},{"type":"text","order":4,"title":"State the conclusion","content":"No. Sarah does not have enough apple juice: she needs $600\\text{ ml}$ but has only $500\\text{ ml}$. This conclusion earns the final A1 mark."}]}],"generatedAt":"2026-

Ratio

Question 16

Ratio Questions

Ratio

Question 16

Ratio Questions