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s.f.).","code":"A"}],"finalAnswers":["15.3"],"generatedAt":"2026-05-07T01:43:33.169Z","modelVersion":"gemini-3-flash-preview"},"tableImages":[],"explanation":{"methods":[{"id":"income_then_profit","label":"Income then percentage profit","steps":[{"type":"hyper_latex","block":{"nodes":[{"latex":"\\htmlData{anchor=remaining}{\\text{Remaining cans}=50-32=18}"},{"text":"So 18 cans are sold at 20p each."}]},"order":0,"title":"Find the remaining cans","description":"Subtract the cans already sold from the total."},{"type":"hyper_latex","block":{"nodes":[{"latex":"32\\times\\pounds0.50=\\pounds16.00"},{"latex":"18\\times\\pounds0.20=\\pounds3.60"},{"latex":"\\htmlData{anchor=income}{\\pounds16.00+\\pounds3.60=\\pounds19.60}"}]},"order":1,"title":"Calculate total income","description":"Convert pence to pounds first: 50p = £0.50 and 20p = £0.20. This total-income calculation earns the first method mark."},{"type":"hyper_latex","block":{"nodes":[{"latex":"\\htmlData{anchor=profit}{\\pounds19.60-\\pounds17.00=\\pounds2.60}"},{"latex":"\\htmlData{anchor=percentage}{\\dfrac{\\pounds2.60}{\\pounds17.00}\\times100=15.294117\\ldots\\%}"}]},"order":2,"title":"Work out percentage profit","description":"Profit is income minus the original cost. For percentage profit, divide by the original cost, not by the income. Setting up this calculation earns the second method mark."},{"type":"text","order":3,"title":"Round the percentage","content":"The first three significant figures are $1$, $5$ and $2$. The next digit is $9$, so round the $2$ up to $3$.\n\n$$\\boxed{15.3\\%}$$\n\nThis is correct to three significant figures and earns the accuracy mark.","highlights":[{"text":"Give your answer correct to three significant figures.","location":"specification"}]}]}],"generatedAt":"2026-07-21T04:05:53.642Z","modelVersion":"gpt-5.6-terra","explanationVersion":"v3"},"options":[]}],"options":[],"explanation":null,"firstAttemptFullMarks":{"percent":73},"walkthroughVideo":null},{"id":"f2405e53-20f4-4ae8-aa89-c4da95a654c9","revisionId":"4f7ebd56-75d1-4337-b434-f730a7ca5e13","questionNumber":"11","questionType":"LA","specification":"","difficulty":2,"difficultyBand":"medium","totalMarks":3,"sourceTitle":"Percentage Change","calculatorUse":null,"isCalculation":true,"parts":[{"id":"614214e2-03f8-4aeb-9b9f-a8f14bce6ae5","label":"0","content":"Karen buys a pack of 8 bottles of water.\nThe pack costs £1.25\n\nKaren sells all 8 bottles of water for 50p each.\n\nWork out Karen's percentage profit.","markscheme":"- Calculate total income: $8 \\times 0.50 = £4$ M1\n- Calculate percentage profit: $\\frac{4 - 1.25}{1.25} \\times 100$ M1\n- Final answer: 220% A1","marks":3,"order":0,"markingRubric":{"totalMarks":3,"points":[{"id":"p1","marks":1,"description":"Calculates the total selling price (£4).","code":"M"},{"id":"p2","marks":1,"description":"Divides the profit (£2.75) by the cost price (£1.25).","code":"M"},{"id":"p3","marks":1,"description":"Final answer of 220.","code":"A"}],"finalAnswers":["220"],"generatedAt":"2026-05-07T01:43:33.169Z","modelVersion":"gemini-3-flash-preview"},"tableImages":[],"explanation":{"methods":[{"id":"percentage_profit","label":"Calculate percentage profit","steps":[{"type":"text","order":0,"title":"Identify cost and income","content":"The **cost** is the £1.25 Karen paid for the pack. Her **income** is the money she receives from selling the bottles. We need the income first, then compare the profit with the original cost.","highlights":[{"text":"The pack costs £1.25","location":"specification"},{"text":"Karen sells all 8 bottles of water for 50p each.","location":"specification"}]},{"type":"hyper_latex","block":{"nodes":[{"latex":"\\htmlData{anchor=conversion}{\\color{@sky}{50\\text{p}}}=£0.50"},{"latex":"8\\times\\color{@green}{£0.50}=\\htmlData{anchor=income}{\\color{@green}{£4}}"}],"highlights":[{"color":"sky","style":"text-color","anchor":"conversion"},{"color":"green","style":"text-color","anchor":"income"}]},"order":1,"title":"Find the total income","description":"Convert 50p to £0.50, then multiply by the number of bottles sold. M1: 8 × £0.50 = £4."},{"type":"hyper_latex","block":{"nodes":[{"latex":"\\color{@green}{£4}-\\color{@orange}{£1.25}=\\color{@sky}{£2.75}"},{"latex":"\\text{percentage profit}=\\frac{\\color{@green}{£4}-\\color{@orange}{£1.25}}{\\color{@orange}{£1.25}}\\times100"},{"latex":"\\text{percentage profit}=\\color{@green}{220\\%}"}]},"order":2,"title":"Calculate percentage profit","description":"Profit is income minus cost. For percentage profit, divide the profit by the original cost, then multiply by 100. M1: use (4 − 1.25) ÷ 1.25 × 100. A1: 220%."}]}],"generatedAt":"2026-07-21T04:10:00.862Z","modelVersion":"gpt-5.6-terra","explanationVersion":"v3"},"options":[]}],"options":[],"explanation":null,"firstAttemptFullMarks":null,"walkthroughVideo":null},{"id":"55874878-cded-40b0-b390-b560f2fccf37","revisionId":"2707f114-24f8-48d5-9786-e01dfa5ac9dd","questionNumber":"12","questionType":"LA","specification":"","difficulty":2,"difficultyBand":"medium","totalMarks":3,"sourceTitle":"Percentage Change","calculatorUse":null,"isCalculation":true,"parts":[{"id":"85fe4218-8bdd-4426-936b-33ad9f6aa8d2","label":"0","content":"Theo buys 24 packs of crisps.\nHe pays £3 for the crisps.\n\nTheo sells each pack of crisps for 50p.\n\nWork out Theo's percentage profit.","markscheme":"- Calculate total income: $24 \\times 0.50 = £12$ M1\n- Calculate percentage profit: $\\frac{12 - 3}{3} \\times 100$ M1\n- Final answer: 300% A1","marks":3,"order":0,"markingRubric":{"totalMarks":3,"points":[{"id":"p1","marks":1,"description":"Calculates the total selling price (£12).","code":"M"},{"id":"p2","marks":1,"description":"Divides the profit (£9) by the cost price (£3).","code":"M"},{"id":"p3","marks":1,"description":"Final answer of 300.","code":"A"}],"finalAnswers":["300"],"generatedAt":"2026-05-07T01:43:33.169Z","modelVersion":"gemini-3-flash-preview"},"tableImages":[],"explanation":{"methods":[{"id":"income_then_profit","label":"Income then percentage profit","steps":[{"type":"text","order":0,"title":"Find the selling income","content":"Theo sells all $24$ packs, so first find his **total income** (the money received from sales). Convert $50\\text{p}$ to £$0.50$ so the money units match the £$3$ cost.","highlights":[{"text":"Theo sells each pack of crisps for 50p.","location":"specification"}]},{"type":"hyper_latex","block":{"nodes":[{"latex":"\\htmlData{anchor=income_setup}{\\color{@sky}{24\\times £0.50}}"},{"latex":"\\htmlData{anchor=income}{\\color{@green}{£12}}"}],"highlights":[{"color":"green","style":"text-color-with-background","anchor":"income"}],"connections":[{"to":"income","from":"income_setup","color":"sky","label":"multiply"}]},"order":1,"title":"Calculate the income","description":"Multiply the number of packs by the selling price per pack. This earns the first M1 mark."},{"type":"text","order":2,"title":"Use the percentage formula","content":"Profit is income minus cost. A percentage profit compares that profit with the **original cost**, so divide by £$3$, then multiply by $100$. Setting up this calculation earns the second M1 mark.","highlights":[{"text":"He pays £3 for the crisps.","location":"specification"}]},{"type":"hyper_latex","block":{"nodes":[{"latex":"\\frac{\\htmlData{anchor=income}{\\color{@sky}{\\text{income}}}-\\htmlData{anchor=cost}{\\color{@orange}{\\text{cost}}}}{\\text{cost}}\\times100"},{"latex":"\\frac{\\htmlData{anchor=values}{\\color{@sky}{12}-\\color{@orange}{3}}}{\\color{@orange}{3}}\\times100"},{"latex":"\\htmlData{anchor=answer}{\\color{@green}{300\\%}}"}],"highlights":[{"color":"sky","style":"text-color-with-background","anchor":"values"},{"color":"green","style":"text-color-with-background","anchor":"answer"}],"connections":[{"to":"answer","from":"values","color":"green","label":"calculate","style":"solid"}]},"order":3,"title":"Calculate percentage profit","description":"Subtract the original cost to find the profit, then divide by the original cost and multiply by 100. This is the A1 mark: 300%."}]}],"generatedAt":"2026-07-21T04:03:50.253Z","modelVersion":"gpt-5.6-terra","explanationVersion":"v3"},"options":[]}],"options":[],"explanation":null,"firstAttemptFullMarks":null,"walkthroughVideo":null}],"subjectCode":"igcse_maths","summaries":[{"id":"61bdae87-69d9-400e-a849-f3614a5f09ef","difficultyBand":"medium","calculatorUse":null,"totalMarks":3,"questionType":"LA","isCalculation":true},{"id":"86b74992-959b-46aa-9078-36351a13a3d6","difficultyBand":"medium","calculatorUse":null,"totalMarks":3,"questionType":"LA","isCalculation":true},{"id":"c0fe0f74-1974-4371-9cb6-bd3c9ae1e453","difficultyBand":"medium","calculatorUse":null,"totalMarks":3,"questionType":"LA","isCalculation":true},{"id":"2a24afd1-e695-4f02-83bf-c807aa126adb","difficultyBand":"medium","calculatorUse":null,"totalMarks":3,"questionType":"LA","isCalculation":true},{"id":"94e8933a-0403-40fb-af1d-2566480f3238","difficultyBand":"medium","calculatorUse":null,"totalMarks":3,"questionType":"LA","isCalculation":true},{"id":"6a5e6c36-4606-4a61-b54e-7ae905438c68","difficultyBand":"medium","calculatorUse":null,"totalMarks":3,"questionType":"LA","isCalculation":true},{"id":"3a2eab83-cd65-4c6e-8a3f-24f642893462","difficultyBand":"medium","calculatorUse":null,"totalMarks":3,"questionType":"LA","isCalculation":true},{"id":"47c4225d-9a70-4d4f-ae04-c2e68e2f28dd","difficultyBand":"medium","calculatorUse":null,"totalMarks":3,"questionType":"LA","isCalculation":true},{"id":"4bdfea9d-e72a-40ea-b162-1d9019a30570","difficultyBand":"medium","calculatorUse":null,"totalMarks":3,"questionType":"LA","isCalculation":true},{"id":"090917f4-34a9-449c-a0c0-60f80fe4a1de","difficultyBand":"medium","calculatorUse":null,"totalMarks":3,"questionType":"LA","isCalculation":true},{"id":"f2405e53-20f4-4ae8-aa89-c4da95a654c9","difficultyBand":"medium","calculatorUse":null,"totalMarks":3,"questionType":"LA","isCalculation":true},{"id":"55874878-cded-40b0-b390-b560f2fccf37","difficultyBand":"medium","calculatorUse":null,"totalMarks":3,"questionType":"LA","isCalculation":true},{"id":"ab590872-483f-4eb4-a04d-e03c53dc0c5c","difficultyBand":"medium","calculatorUse":null,"totalMarks":3,"questionType":"LA","isCalculation":true},{"id":"02da1f72-d40a-49e1-a99b-3a2251ce310c","difficultyBand":"medium","calculatorUse":null,"totalMarks":4,"questionType":"LA","isCalculation":true}],"title":"Percentage Change","topicId":"b5e07209-ce7f-4f40-9728-24edf9a1c0cb","topicSidebar":"$L3a","topicSlug":"grade-3-3-7-percentage-change","topicTitle":"Percentage Change"}]}],"$L3b","$L3c"]}]