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As a decimal multiplier, $108\\%=1.08$.","highlights":[{"text":"increased by 8%","location":"specification"}]},{"type":"hyper_latex","block":{"nodes":[{"latex":"\\htmlData{anchor=cost}{\\color{@sky}{1.62}}=\\htmlData{anchor=multiplier}{\\color{@amber}{1.08p}}"},{"latex":"p=\\dfrac{\\color{@sky}{1.62}}{\\htmlData{anchor=divisor}{\\color{@amber}{1.08}}}"},{"latex":"p=\\htmlData{anchor=pounds}{\\color{@green}{\\pounds1.50}}"}],"highlights":[{"color":"sky","style":"text-color","anchor":"cost"},{"color":"amber","style":"text-color","anchor":"multiplier"},{"color":"amber","style":"text-color","anchor":"divisor"},{"color":"green","style":"text-color","anchor":"pounds"}]},"order":1,"title":"Undo the increase","description":"Let p be the petrol price before the increase. Calculating 1.62 divided by 1.08 earns M1; the resulting original price £1.50 earns A1."}]}],"generatedAt":"2026-07-21T03:56:09.756Z","modelVersion":"gpt-5.6-terra","explanationVersion":"v3"},"options":[]}],"options":[],"explanation":null,"firstAttemptFullMarks":{"percent":67},"walkthroughVideo":null},{"id":"3794d92d-ea51-46b5-ba4b-71dad3a02adc","revisionId":"bd61f8eb-df23-4dec-b9fc-aca212924b03","questionNumber":"4","questionType":"LA","specification":"","difficulty":1,"difficultyBand":"easy","totalMarks":2,"sourceTitle":"Reverse Percentages","calculatorUse":null,"isCalculation":true,"parts":[{"id":"3716b7f7-b728-4393-8255-e4f01d18b730","label":"0","content":"In a sale, normal prices are reduced by 25%. \nThe normal price of a coat is reduced by £12\n\nWork out the normal price of the coat.","markscheme":"- Award method mark for equating 25% to 12 or $12 \\div 0.25$ M1\n- Final answer of 48 A1","marks":2,"order":0,"markingRubric":{"totalMarks":2,"points":[{"id":"p1","marks":1,"description":"Identifies that 25% is equal to £12.","code":"M"},{"id":"p2","marks":1,"description":"Final answer of 48.","code":"A"}],"finalAnswers":["48"],"generatedAt":"2026-05-07T01:57:05.230Z","modelVersion":"gemini-3-flash-preview"},"tableImages":[],"explanation":{"methods":[{"id":"percentage_division","label":"Find 100% from 25%","steps":[{"type":"text","order":0,"title":"Identify the percentage","content":"The £12 reduction is **25%** of the normal price. So we need to find the value of $100\\%$ when $25\\%=£12$.","highlights":[{"text":"normal prices are reduced by 25%.","location":"specification"},{"text":"reduced by £12","location":"specification"}]},{"type":"hyper_latex","block":{"nodes":[{"latex":"\\htmlData{anchor=percentage}{\\color{@sky}{25\\%}}=\\htmlData{anchor=decimal}{\\color{@sky}{0.25}}"},{"latex":"\\text{normal price}=\\frac{\\pounds12}{\\htmlData{anchor=divisor}{\\color{@sky}{0.25}}}"},{"latex":"\\text{normal price}=\\htmlData{anchor=answer}{\\color{@green}{\\pounds48}}"}],"highlights":[{"color":"sky","style":"text-color-with-background","anchor":"percentage"},{"color":"sky","style":"text-color-with-background","anchor":"divisor"},{"color":"green","style":"text-color-with-background","anchor":"answer"}]},"order":1,"title":"Calculate the whole price","description":"25% is £12, so divide £12 by 0.25 to find the normal price. This earns M1; £48 earns A1."}]}],"generatedAt":"2026-07-21T03:54:29.198Z","modelVersion":"gpt-5.6-terra","explanationVersion":"v3"},"options":[]}],"options":[],"explanation":null,"firstAttemptFullMarks":{"percent":65},"walkthroughVideo":null},{"id":"18db6891-21c9-4d67-88ae-625c52c418f6","revisionId":"28f43471-742d-4870-a7db-3d9532e68af0","questionNumber":"5","questionType":"LA","specification":"","difficulty":1,"difficultyBand":"easy","totalMarks":2,"sourceTitle":"Reverse Percentages","calculatorUse":null,"isCalculation":true,"parts":[{"id":"f27298d6-a8ce-45ba-a333-7a44ac79676d","label":"0","content":"In a sale, the normal price of a TV is reduced by 20%. \nThe sale price of the TV is £660\n\nWork out the normal price of the TV.","markscheme":"- Award method mark for $660 \\div 0.8$ or equating 80% to 660 M1\n- Final answer of 825 A1","marks":2,"order":0,"markingRubric":{"totalMarks":2,"points":[{"id":"p1","marks":1,"description":"Uses a correct method to find the original price, e.g., $660 \\div 0.8$.","code":"M"},{"id":"p2","marks":1,"description":"Final answer of 825.","code":"A"}],"finalAnswers":["825"],"generatedAt":"2026-05-07T01:57:05.230Z","modelVersion":"gemini-3-flash-preview"},"tableImages":[],"explanation":{"methods":[{"id":"decimal_method","label":"Divide by the sale percentage","steps":[{"type":"text","order":0,"title":"Find the percentage left","content":"A reduction of $20\\%$ leaves $80\\%$ of the normal price. As a decimal, $80\\%=0.8$.","highlights":[{"text":"reduced by 20%","location":"specification"}]},{"type":"hyper_latex","block":{"nodes":[{"latex":"\\htmlData{anchor=start}{660=0.8\\times\\text{normal price}}"},{"latex":"\\htmlData{anchor=result}{\\text{normal price}=660\\div0.8=\\pounds825}"}],"connections":[{"to":"result","from":"start","color":"sky","label":"divide both sides by 0.8","style":"solid"}]},"order":1,"title":"Divide to reverse reduction","description":"The sale price is 0.8 times the normal price, so divide by 0.8 to undo this. M1: setting up 660 divided by 0.8 earns the method mark. A1: the normal price is £825."}]},{"id":"percentage_method","label":"Find 1% then 100%","steps":[{"type":"text","order":0,"title":"Identify the sale percentage","content":"After a $20\\%$ reduction, the sale price is $80\\%$ of the normal price. So £660 represents $80\\%$.","highlights":[{"text":"reduced by 20%","location":"specification"},{"text":"The sale price of the TV is £660","location":"specification"}]},{"type":"hyper_latex","block":{"nodes":[{"latex":"\\htmlData{anchor=eighty}{80\\%\\text{ of normal price}=\\pounds660}"},{"latex":"\\htmlData{anchor=one}{1\\%\\text{ of normal price}=\\pounds660\\div80=\\pounds8.25}"},{"latex":"100\\%\\text{ of normal price}=\\pounds8.25\\times100=\\pounds825"}],"connections":[{"to":"one","from":"eighty","color":"sky","label":"divide by 80","style":"solid"}]},"order":1,"title":"Find 1% then 100%","description":"Find the value of 1%, then multiply by 100 to get the normal price. M1: identifying £660 as 80% earns the method mark. 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