r","label":"Fraction Multiplier Method","steps":[{"type":"text","order":0,"title":"Analyze the ratio","content":"First, let's identify how the three paint colors are related using the given ratio:\n\n$$\\text{Blue} : \\text{White} : \\text{Yellow} = 5 : 3 : 2$$\n\nWe are given the actual amount of **white paint** used:\n$$\\text{White} = 450\\text{ ml}$$","highlights":[{"text":"blue paint, white paint, and yellow paint in the ratio $5 : 3 : 2$","location":"specification"},{"text":"Sarah uses $450\\text{ ml}$ of white paint.","location":"specification"}]},{"type":"hyper_latex","block":{"nodes":[{"latex":"$$$\\text{Blue} = \\htmlData{anchor=frac-blue}{\\frac{5}{3}} \\times \\text{White}$$"},{"latex":"$$$\\text{Blue} = \\frac{5}{3} \\times \\htmlData{anchor=white-val}{450\\text{ ml}}$$"},{"latex":"$$$\\text{Blue} = \\htmlData{anchor=blue-ans}{750\\text{ ml}}$$"}],"highlights":[{"color":"sky","style":"text-color","anchor":"frac-blue"},{"color":"amber","style":"text-color","anchor":"white-val"},{"color":"green","style":"box","anchor":"blue-ans"}],"connections":[{"to":"blue-ans","from":"white-val","color":"sky","label":"multiply","style":"solid"}]},"order":1,"title":"Find blue paint multiplier","description":"Since the ratio of blue to white is $5:3$, the amount of blue paint is exactly $\\frac{5}{3}$ of the amount of white paint. We multiply the white paint by this fraction."},{"type":"hyper_latex","block":{"nodes":[{"latex":"$$$\\text{Yellow} = \\htmlData{anchor=frac-yellow}{\\frac{2}{3}} \\times \\text{White}$$"},{"latex":"$$$\\text{Yellow} = \\frac{2}{3} \\times \\htmlData{anchor=white-val2}{450\\text{ ml}}$$"},{"latex":"$$$\\text{Yellow} = \\htmlData{anchor=yellow-ans}{300\\text{ ml}}$$"}],"highlights":[{"color":"purple","style":"text-color","anchor":"frac-yellow"},{"color":"amber","style":"text-color","anchor":"white-val2"},{"color":"green","style":"box","anchor":"yellow-ans"}],"connections":[{"to":"yellow-ans","from":"white-val2","color":"purple","label":"multiply","style":"solid"}]},"order":2,"title":"Find yellow paint multiplier","description":"Similarly, the ratio of yellow to white is $2:3$, so the amount of yellow paint is $\\frac{2}{3}$ of the amount of white paint."},{"type":"text","order":3,"title":"State the final answers","content":"By directly applying these fractional multipliers to our known volume of white paint ($450\\text{ ml}$), we find:\n\n* **Blue paint:** $750\\text{ ml}$ (awarded A1)\n* **Yellow paint:** $300\\text{ ml}$ (awarded A1)\n\n*(Note: Finding the value of a single share, $450 \\div 3 = 150\\text{ ml}$, awards the method mark M1)*"}]}],"generatedAt":"2026-06-12T14:31:43.705Z","modelVersion":"gemini-3.5-flash","explanationVersion":"v2"},"firstAttemptFullMarks":{"percent":75}},{"id":"42483e20-3be3-4e2d-8c86-abb05001b6f8","revisionId":"ed8a5fa8-9cb4-45f5-a1e2-42ba6e89358d","questionNumber":null,"questionType":"LA","specification":"$$PQR$ is a straight line.\n\n![A straight line segment with points P, Q, and R marked. P is on the left, Q is in the middle, and R is on the right. There are small vertical tick marks above each letter.](https://assets.mathsgenie.co.uk/questions/ce73f5af-eede-4e1a-ba66-c40c10030816.png)","difficulty":2,"difficultyBand":"medium","totalMarks":3,"sourceTitle":null,"calculatorUse":"non_calc","parts":[{"id":"0ab2ab2c-ff6b-4316-b23b-38fb44baf02e","label":"a","content":"The length of $QR$ is five times the length of $PQ$.\n\n$QR = 150$ cm.\nWork out the length $PR$.","markscheme":"- Calculate $PQ$: $150 \\div 5 = 30$ M1\n- Calculate $PR$ method: $150 + 30$ M1\n- Final length $PR$: $180$ A1","marks":3,"order":0,"markingRubric":{"totalMarks":3,"points":[{"id":"p1","marks":1,"description":"Evidence of dividing 150 by 5 to find PQ.","code":"M"},{"id":"p2","marks":1,"description":"Evidence of adding the two segment lengths (150 + 30).","code":"M"},{"id":"p3","marks":1,"description":"Correct final length of 180 cm.","code":"A"}],"finalAnswers":["180","180 cm"],"generatedAt":"2026-05-06T14:0

Ratio

Question 5

Ratio Questions

Ratio

Question 5

Ratio Questions